I was able to get the front mount changed however I can't seem to get the rear mount out from underneath the car. Surely it comes out the bottom? I fought with it for like 2 hours with no luck.

Could anybody provide some insight on how I get the rear transmission mount out?

It is the 99 Isuzu 5 speed by the way.

You take it out through the wheel well or the top. There is the 13mm bolt that goes through the bushing that has to be taken out from the BACK of the mount. Then there are 3 13mm bolts attaching it to the trans. 2 of them face up in the engine bay and 1 faces outwards towards the drivers side of the car that has to be taken out through the wheel well. I normally unbolt the brake master cylinder and tie it out of the way to make my life easier.

Yeah, I was able to get all of the bolts out. I just couldn't wrestle the mount out of there. It almost comes out through the wheel well but it gets could on the bracket.