I'd agree with the others to look at the flipper opto boards, but if you'd tried 3 sets (all of them with clean optos correct?), you can pretty well eliminate that as the issue. The next place would be to look at board issues, but you've eliminated board problems by swapping in good known working boards. If you've indeed already replaced the CPU, Driver board, flippertronics board, flipper opto boards, and even the transformer with known good working ones (plus new coils, EOS switches), you've eliminated all of them as the issue. That only leaves me to think you've got a wiring problem somewhere.
You might try swapping ribbon cables to eliminate those as an issue since they carry the data for the logic. Bad ribbon cables can cause all sorts of weird problems.