So: there is a Folk Opera episode entitled Thumbelina in the Bamboo Tube. This is Nang Ut, who is closer to Doll i’ the Grass than she is to the Thumbling tale type. I was pleased to find this with subtitles in English (and lots of other languages, but mostly English).
Two fairies are nearly sentenced to death for the crime of falling in love (“the grave sin of flirting!!!”), but instead they are sentenced to be reborn as mortals. Both will suffer before finding each other again, but the girl in particular will be born poor with “a tiny and hideous appearance” and will have to labor in the fields and sleep in a bamboo tube. She’ll become beautiful when someone compassionate loves her.
The man, reborn as the (very pretty, very makeup-wearing) third son of the Emperor, is choosing a wife. She must be beautiful, educated, skilled, and well-mannered, as she will be First-rank Princess Consort. (I don’t know why, since he’s the youngest.) There are some princesses waiting for him to choose one of them, but he doesn’t want to marry just for beauty, and tells his father that he has to turn them all down. Most of the princesses accede to this, but the Princess of So is furious. She is invited to stay, however, because her country’s very powerful and they don’t want to anger her. She’s in love with Third Prince, and his brothers and their consorts want him to marry her. They begin to plot together.
Meanwhile, the prince prays, and has a vision of his beloved from his past life. They had a previous affinity in Paradise. “A predestined marriage with karmic obstructions.” I thought these two were arrested for falling in love. 
“The watermelon field is my home.” Little Thumbelina is my name.” Okay! She fades away. He’s distraught. His servants run in, saying she’s here, but it’s actually just one of them dressed up as a woman. (This is our comic relief, guys.) They beg the prince not to punish them because they were just trying to cheer him up. He tells them to just come along as he travels out to look at flowers.
They sit down by a field and the now-thirsty prince sends his two servants to find water. They argue with each other and pray for rain (comedy alert). PLEASE STOP SINGING AND GET TO THE PLOT. Then they find watermelons, and when the prince comes to see what’s taking them so long, they give him a melon. However, right after they split it open, he says they must find the owner. It’s not a wild melon because there’s a proper garden with rows. (Yes, after they start breaking open watermelons, he notices this.) 
The owner, Third Prince assumes, must be a kind-hearted, industrious and beautiful girl. The servants point out that it could just as easily be an old lady. The prince says they have to find the owner and pay for the melon. The prince thinks she must be hiding and tells the eunuchs to head back. 
Just then, they hear a voice calling out. The voice belongs to a tiny girl, set up in a weird-looking tiny bamboo hut chair thing.

Sorry for the low quality, but what is that?
She asks them to pay for the melon. At first the servants can’t find her because she’s so small; then they’re terrified, thinking she’s a demon, and faint dead away. The Prince comes looking for them, again, and is also frightened by her appearance.
“Yes, I’m a freak and I’m ugly. That’s why I keep myself in the forest, befriend trees and plants, rest in the green bamboo tube at night, labor to grow melons during the day and live alone; such is my ill fate.”
The prince quickly feels sorry for her and asks her story. She explains that her mother died in childbirth after seeing her child so small. The girl’s father abandoned her in the melon garden and became a monk. The prince decides to marry her and take her home, and she rides to his palace inside his long sleeve.
Rumors spread that the prince has taken a wife. Princess So is not happy that he scorned her in favor of an ugly, finger-sized woman, and a peasant to boot. In conference with the older princes and their wives, it is suggested that Nang Ut is a fiend who will destroy the dynasty. However, they reassure themselves that she can’t possibly have the virtue and beauty required of a princess. They speak to the emperor and empress and arrange a contest.
The prince is frightened that Nang Ut can’t possibly cook a meal. “Little One, you can’t even hold a pot. How can you cook? You’d get burnt as soon as you went to the kitchen.”
Honestly, they are really cute together in this scene. She jumps onto his hand to say goodnight. There is lots of singing. (It is a musical.) After he goes to bed, Nang Ut prays (“Help me out of this karmic obstruction!”) and a fairy appears (why? Who is this? What’s going on?). The fairy gives her a jewel. Nang Ut passes it on to the prince; at the contest, he cracks the jewel open and it creates a tray of amazing food. The fairy also intervenes in the contest by making the other wives’ meals less tasty. This strikes me as cheating, but Nang Ut wins.
The prince tries to say that Nang Ut doesn’t care about being First Rank Princess Consort, but the other siblings insist on a second contest, this one a set of royal robes for the emperor and empress.
Meanwhile, the Princess of So is preparing an army and plots to to kill Nang Ut. Nang Ut has a dream about this or somehow senses that she’s in danger, I guess? She and the Prince begin to pray, and once more the fairy appears. This time she gives them a gem which will become royal robes, a nectar that will make someone look as beautiful as a fairy, and a golden hairpin that will become a heavenly lute.
Once more, the fairy’s magical robes win the contest (and the fairy sabotages the brothers’ entries). But the Princess of So’s army is here. “Woe to us!” 
As per their agreement with the evil princess, the royal siblings demand that Third Prince go out to join the fighting. His pickiness ruined everything! He graciously tells his parents that he has to go and fight, despite their protests that he’s too inexperienced. He’s an intellectual, not a warrior.
The prince comes out on the wall carrying Nang Ut in what seems to my educated eye to be a birdcage (oh, and she was living in a dollhouse inside the palace, too). He negotiates with the besieging army and Nang Ut speaks up, startling the others, to challenge the enemy general. If he can eat all the rice in her little pot, then he wins. (Wait, where’d they get the pot from?) The pot, of course, refills itself automatically, and the general gets angry. (Still confused but okay.) 
“Devil’s magic is at work here! Deploy the troops!” The army charges and Nang Ut tells the prince to use the golden hairpin. It becomes a lute and its music confuses the soldiers, sends them into despair and fills them with the desire to go home. They all collapse. The war is over before it begins. 
Princess So: “I’ve been to many perilous battles and never flinched from swords and arrows” (pretty hardcore) “but now I must accept defeat and drop my swords. Kill me, then! So will be ruined and filled with tears.”
But Nang Ut has mercy and makes an alliance with her. Shamed, the princess of So blames the two princess consorts for everything. There are so many princesses in here. 
With war averted, the beauty contest ensues. The princess consorts come out, bow, dance, respectfully greet the king and queen. The queen asks for Nang Ut, but the Prince is worried.
“They’re so beautiful I don’t know what to do!” he says to Nang Ut, who is back in his sleeve.
“My love, did you forget already? Pour this nectar water on me and you’ll witness something incredible.”
Burst of smoke. There’s Nang Ut, full size. The prince doesn’t recognize her at first (“Miss, why are you here in my palace? Darling Thumbelina, where are you?”) but then they run up to join the contest.

The King: “She’s like a fairy from heaven!”

Even the princes and their wives have to admit that Nang Ut is worthy to be First-Rank Princess Consort. They are about to be punished for their treachery,  but our heroes ask for leniency on their behalf. Good for you, guys. The king decides to retire and live in peace, farming on a mountain. They ask to go with him, but he goes off on his own. With that, Third Prince and Nang Ut become the new rulers. All very happy. All singing. So much singing.
Start watching it here.
(Originally posted on Tumblr.)

I recently read The Types of the Irish Folktale by Sean ´O Súilleabháin and Reidar Th. Christiansen. This led me to the Schools' Collection - an effort by Irish folklorists to preserve old traditions by enlisting schoolchildren.

Fortunately for me, they are now in the process of digitizing this database! However, it took me a while to decipher the way the type index listed the examples of Type 700 found in the Schools collection. The website uses the format “The Schools’ Collection, Volume ----, Page ---.

A few interesting trends showed up as I went through this. Probably the most prominent trend is that I can't read Gaelic. Especially handwritten Gaelic. So much handwriting.
 
Variants of Thumbling

• Micklen.
• Wee Jack
• Micheal Beag
• Timidín na Luaithe (Gaelic, unable to read). Luaithe – nimble, speedy.
• Toimidín na Luaithe. Gaelic, unable to read.

 
Variants of Thumbling that use the name “Tom Thumb”

• “Tom Tum”
• “An Old Story.”
• Tom Thumb. (This is actually just the English tale copied down.)
• Tomás na hOrdóige. Gaelic, unable to read.
• Tomas na hOrdóige.
• Tomás Beag na hOrdóige. Gaelic, unable to read.

 
Variants of the Young Giant

• “A Story.” Uses the name Tom Thumb.
• The Dwarf who Grew Up. Uses the name Tom Thumb.  
• Variant of the Young Giant. Uses the name Tom Thumb.

 
Other Tale Types

• Bolgaidín
• Boiligín agus an tSeanbhean (Boiligin and the old woman)
• Boiligín agus an tSeanbhean
• Boiligdín
• Boilgidín 
• An Bhean a Thug léi Boilgín 
• A story in which a girl is swallowed by a cow.

 
Gaelic, unable to read

• Gaelic story. 
• An Gobán Saor. 
• Scéal faoi Oiread Ceann Mordhóig 
• http://www.duchas.ie/en/cbes/4622975/4619389
• Scéal Greannmhar
  
• http://www.duchas.ie/en/cbes/4427991/4364921/4469157
• Cathaoir Shúgáin. 
• Séimidh.
• http://www.duchas.ie/en/cbes/4428372/4400921

 
Does not match
These were listed in the Type Index, but do not seem to be variants of Type 700. I may have made a mistake in transcription here.

• 0059 229. This entry appears to be a description of churning.
• An tSlí a mBíonn a Fhios ag Muintir na hÁite ón nGréin cén Saghas Aimsire a Bhíonn air.
• 0089 161 Riddles.
• “A Funny Story.” 
• 0160 217 Discussion of "fairy fort." Transcribed wrong?
• Whirlwind in May.
• 851 274. 

Unable to find

• 250 377
• 256 287.
• 257 665
• 260 141
• 280 218
• 322 143
• 348 188
• 352 250
• 375 286
• 402 754
• 538 534
• 551 56
• 551 137
• 613 407.
• 624 357
• 640 221 – found, but currently unavailable.
• 728 205
• 743 350
• 882 427
• 1012 6
• 1018 6
• 1170 447
• 1207 23
• 1213 30
• 1270 245
• 1323 551
• 868 323 
• 938 466