Could be it's not anything wrong with the engine or tranny itself - but perhaps old original leaky vacuum lines, misadjusted throttle cable, etc, that were already on the sedan.
When I got my first 87, it had the infamous "mule kicking the rear bumper" hard shift at anything other than WOT. It was a long process, first chasing down all the vacuum leaks due to cracked hard lines and ancient brittle rubber hose. Then doing the tests in the FSM and discovering the vacuum control valve was long gone and required replacement, plus checking the vacuum at other points and the final vacuum signal to the tranny. After that came adjusting the throttle cable and the throttle linkages, plus the feedback cable from the trans. And the final piece of the puzzle was having the tranny pulled out and all those 20 year old leaking seals replaced. At the end, I had a properly shifting tranny and a car that would run like a scalded ape.
That's another possibility - if the tranny hasn't had the seals replaced in some time (or never), especially around the oil pump, it could be that something got "disturbed" during the transplant process , and some seals, either vacuum or hydraulic, aren't doing their job any more.
FWIW, my tranny guru of over 12 years back in NC says these particular trannys are IHHO the toughest auto trannys ever made. When I asked about getting the tranny I mentioned above rebuilt, convinced there was something significantly wrong with it, he declined - he said at most, it would just need to be disassembled and have all the seals replaced, then properly adjusted - that it was rare indeed to find something mechanically wrong with one of them, unless it had been badly abused. Turns out he was spot on.