Magnum 5.9 help
The 360's converter must be from the same trans in order to fit the one you have. OR read as, "A 727/518 converter will not fit into the 904/500 trans.)
If that 360 you have now had a 727/518 behind it to start with, then that is the trans to use or get for the car.
If you have a 904/500 trans, you will need a neutral balance converter and a B&M flex plate to mate the external balance engine to the neutral balanced converter.
I do not know if the smaller 904/500 trans was connected to the 360 with a external balanced converter. I do not think this was done at the factory.