Cv25s engine backfire

If what you are saying is that when you reach maximum rpm the car backfires, first be aware that most ignition modules have two sections--one for low rpm and one for high rpm. Could be bad ignition module. Also possible that some tune up item (plug wires, dist. cap) is bad, or that the engine is running too lean at high rpms (bad fuel pump, dirty filter, etc.)

Stuck EGR valve? Vacuum leak? Ignition module low rpm section bad?

This could be anything from bad ignition to timing to bad fuel supply (lean) to bad valves in engine. Run compression test to eliminate worst case, check both ignition and cam timing, vacuum leaks, ignition module.

I think you have a valve problem. Need to remove valve covers and look for loose or broken rocker arms. If an exhaust valve does not open because the rocker is broken the trapped combustion gasses will revert through the intake when the intake valve opens. This can interupt the intake flow to other cylinders and prevent starting.

I know you mentioned the EGR valve has been replaced, but you may have a bad 'new' part. I know the car is electronic, but has anyone checked its ignition timing (timing belt been looked at, I know it only has 77k on it). Is the fuel pressure regulator OK and it vacumm supply?

have you checked to see if you have a bad came or lifter. that would make it backfire. if it kind of spits fuel it maybe cam. if it throws fire than it could be timing like a bad chain.

1989 Kohler 20 backfires through the exhaust. What are the possible causes?

intake leak or exhaust leak depending; most likely intake 95%