360s are all the same from 1972-end of production (1991?, the crank is different 71 and prior). AMCs are externally balanced, you MUST use a 360 balancer and 360 flywheel/flexplate.
As long as you're using factory pistons and rods, then stock replacement pieces will work, and balance will be acceptable. If you have aftermarket pistons, then the weight may be different from the factory piston and you should have the whole assembly balanced. Balancing will also affect the longevity of the engine, particularly the main and rod bearings. A balanced assembly spins smoother, so it will last longer. If you have it balanced, the machine shop will need the crank, flywheel, balancer, rods/pistons, and at least one set of rings and rod bearings. They make all the piston/rod assemblies match the lightest one, then they take the weight of a piston/rod/ring/bearing assembly and put "bob weights" on each rod journal and spin the crank with the flywheel/balancer attached to simulate a running engine. They then add or remove weight from the flywheel and balancer so the whole assembly spins smoothly.
The 304 balancer and flywheel/flexplate would take considerable modification to balance to a 360, because the 360 pistons are bigger, and therefore heavier.
For a factory damper: www.damperdoctor.com
Flywheel: http://www.omix-ada.com/jeep-parts/replacement/transmission-parts/manual/jeep-clutch-flywheel-parts/jeep-flywheel/flywheel-72-86-jeep-cj-models.html
I think MC here at Bulltear is an Omix-Ada distributor. You might PM him and see if you can get a better price.
Bob
tufcj