360 4-speed manual transmission?

1974 and 1975 were the only year I know of as stated above for the 360 4 speed . As far as putting a 4 speed setup behind one, no problem, you will just need a flywheel that is balanced for it. I got mine at 440 source, I believe there around $150 new, and come with weights so it can be used either zero balance or external balance which is what 360's were stock. I may be wrong, but I thought the 73 340 was external balance as well, but not positive on that.

You are correct, 73 340 and 360 have a different balance.
If you need a sfi flywheel mcleod sells a nice one that you can use on any engine, just change the balance weight.
FYI magnum 360 is balance different from LA 360.