Old vs New 360/5.9

One thing you have to watch is that the Magnums are "out of balance" DIFFERENTLY than the equivalent LA, IE a 360LA uses different converter/ flywheel weighting than does a 5.9 magnum.

BM makes specialty weighted stuff for them, and "if you are tricky" you could even use the 360 mag flex plate (which is weighted) against a neutral converter. This is not only different weighting than a 360LA but different OEM strategy, as a 360LA used a "neutral" flex plate and a weighted converter.