The flexplate and flywheel are essentially the same thing. It bolts to the back of the crankshaft. It looks like a big gear on the back of the motor. The starter turns the flywheel/flexplate to turn the motor. Typically, it's referred to as a flexplate on an automatic tranny, and a flywheel on a manual. the flexplates are usually thinner than the flywheels.
The flywheel/flexplate helps balance the rotating assembly, and the 360s need the weight distributed differently than the 304 to balance it. This is why you can't use 304 flywheel. As far as balancing one, I don't know of any way to do it. I think you have to buy a flywheel for the 360.
77 CJ-7- AMC 360, Edelbrock cam, MC2100, Fenderwells, CJ T18/D20, Chevy D44/EB 9" rear, Trutrac f/r, 4.11, SOA, 1.25 lift shackles, 35x12.50 BFG KM2s, Shackle Reversal