On a seed where the desired spread appears multiple times(ex: Frame 32, 34, 36, ect), will they all yield the same wild Pokemon? Like, say if I'm headbutting trees, and I get the wanted IV spread, but the Pokemon is a Hoothoot rather than Pineco, will all of those spreads always yield Hoothoots? I know the Nature, Gender, and IVs are always the same for all the frames sharing the same spread, but do they also share the same Pokemon?
No. You have to check the encounter slots for every frame. All of them are different.
EDIT: I'm not completely sure about headbutting trees, but for the others, this is the way to go.