well AFAIK just swapping drive wont work? or will it? i thought the drive "key" or similar would not work with another PS3, locked to the ps3 unit it shipped with, i might be wrong tho,
about where the fw is stored, on newer consoles its partially on the hard drive but "core os files" is stored on a flash on the MB, NAND or something like that, and that would be quite hard i imagine to swap, and no idea if it would actually work,
you could get the YLOD MB repaired imo, pref re-balled at professionals (expensive but is more reliable) or alternative re-flow it with heatgun method (cheap and probably less reliable then re-balling it, neitherless it worked for alot of people and if done right the ps3 could run for years)
Hope it clears somethings up, Good Luck.