The original flex plate won't work because it's not balanced properly for the post-1982 engine. (It's 28oz instead of 50oz like the Explorer engine).
You can either have a machine shop rebalance it or you can get ahold of Art Carr at 800-278-2277 and ask for P/N23115 Mustang II 141 tooth 50oz. imbalance Flex Plates for putting a 5.0L H.O into a Mustang II with a C4.
If you do one of those two things, the engine will bolt up (also use the '96 Explorer harmonic balancer, not your stock one).