I'm pretty sure you have an ignition problem. From the sound of things your pick up coil is going bad, and the heat aggrevates the problem, which is a classis symptom. You can force the failure mode by thermal shocking the pick up coil and the module to determine which one is causing the problem, but my money is on the pick up coil. Do this:
1. Let the engine get cold, so tha the problem is not happening.
2. Pull the cap, get a heat gun and heat up the pick up coil. Try to heat the pick up coil and not the module. Put an omh meter across the pick up coil leads and see if the resitance makes a dramatic change while you heat the coil. Copper has a thermal coeffcicent of resistance, but ti is veyr small, so you should see very small changes. If you see changes on the order of 100's of ohms or higher, you have a bad pick up coil.
OR, just change the thing and be done with it. Cams don't get worse as the engine heats up, and you have tried enough good carbs to eleminate that problem. Heat induced probelems are almost always electrical related, and heat induced ignition problems on electronic ignitions are almost always the pick up coil, followed by the module.