Aside from getting a mechanic to do this or a new car, your best bet at this point is to pull the tranny out of the bad one while all the body panels are off which will be easier, then pull the panels of the one you replaced them on with the bent frame, pull the good tranny, put it in the other while the panels are off, then put your good panels back on the newer one without the frame damage. Safety first.

Good luck man.