904 tranny
If it truly is a 340 car it should have a 727 but like Myron said as old as it is anything could have been changed out and the 904 will do the trick just fine if prepped right. The only problem is the statement by the owner that he says it's been worked over but doesn't know what was done. How can you know something's been worked over and not know anything of what was done??? Big red flag IMO. So many cars get passed off as having bigger engines and more/better performance parts than they really do you have to do your homework good to make sure what your buying is what it's supposed to be.