early A body engine swap

Both transmission and rear axle have been changed by the previous owner, so I don't have any facts about the installation available. I suspect that at least the axle is in stock location since car seems to have stock rear suspension, but naturally angle of the axle could be different than it should be. Can you tell anything about the trans crossmember / mount from the pictures?
Third picture down
t3-jpg.jpg

looks to me like the mount - i.e., the rubber biscuit - might be broken. Not sure. Try putting a jack under the rear of the trans and raising it up, see if the rubber biscuit is separated.

To answer your question, that does appear to be the original trans crossmember and mount.

Exhaust routing is pretty funky. There's room for the tailpipes to be routed over the axle, except your rear end has been braced, so I don't know if they'll clear the braces.