Like Zombie, I'm not sure what A MIGHTY WIND is satirizing, though. I don't think it's much of a parody, either; I'd classify it just as a regular comedy. Haven't seen BEST IN SHOW.
BEST IN SHOW would fit into the same category as A MIGHTY WIND, although the humour and overall tone is more over the top and obvious. I kind of agree that 'parody' doesn't seem that accurate either, to describe them... it's easy to get lost in pidgoen-holing stuff.