The input shaft spline count changed around '66-67
I think you can install a later year input shaft in the trans and use the more common '67 and up torque converters. The 360 balance issue can be handled with the special B&M flexplate or a correctly counterbalanced torque converter. The older 360 and Magnum 360 used different counterbalance weights.

Call John Cope at Cope racing transmissions to verify compatibility.

I think (been awhile) that the 340/360 motor mount ears on the drivers side are about 1/2" further back (or forward) from the 318, and the drivers side boss for the lower engine to trans strut is forward a but requiring a spacer and longer bolt. I think on my truck I just ended up having one of the motor mounts turned sideways to make up the difference? That was back around 1980, so getting hard to remember.