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Bulbapedia says it's determined by an "independent value", so how does that value work? Is it simply a variable that's randomly set to something from 0 to 27? How do they make sure Unowns don't change form when transferred from generations 2 or 3 to a newer game? Please don't question my curiosity.

It's random, but it isn't. Like in DPPt each room in the Solaceon Ruins had each form of Unown while the Unown in the Ruins of Alph have a random form each time you encounter them(excluding ! and ?)
I know Gen 2 based it on DVs and Gen 3 based it on PID, but I've not the faintest clue aside from that it's a unique identifier that's also used for various alternate forms of Pokemon, specifically Deoxys, Burmy, Wormadam, Shellos, Gastrodon, Giratina, Shaymin, Arceus, Rotom, and Pichu.
There's a page on Bulbapedia about it but information about how wild Unown are generated seems to not exist. I'll have to keep looking for more information.

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Alternate forms are stored at offset 0x40 of the Pokémon structure. Each form follows the pattern of index << 3 where index starts at zero for the main form.

source and table for Unown forms