I have done several tranny swaps it could be many things , I know the jack shaft is year specific they changed it in 94 , make sure you have the right part . Whenever you do something like this you have to pick a model year and get the right parts. Like said in a earler post pull the plugs and start there , does it turn over correctly ? check your main ground , engine alignment is very important ,I have had to run larger ground wires in the past .Start there and keep us posted.

 

Not that this will fix the problem,but if the shop is so "very,very,very reputable"why cant they find the problem???

 

One more thing to check is the jackshaft support (boss) in the primary cover. There were different primary covers made which will bolt up fine but the boss in the cover for the jackshaft support are different sizes. You could have a mismatch here meaning a larger bushing in the cover than the jackshaft size that would allow the jackshaft too much side movement, could apply here from what you describe.