I think I'm at the "wild ass guessing" point now that you've cleaned your tank, petcock and carb.
You say the amp meter is showing a very high + reading when the engine is running above an idle and about 1/4 the way above zero when it's idling?
That sounds like a voltage regulator problem or possibly a low battery voltage problem.
Even with a new battery, if the wiring connections at the batteries terminals are not making good contact, that might cause this.
What I'm thinking is, if the voltage in the system is too high, it might overheat the ignition coil. The running speed above idle will cause the coil to be energized more often so the likelyhood of it overheating is greater.
On your next test ride, when the engine dies it might be worth the trouble to reach a finger up and place it on the side of the coil.
If your finger gets burned you might be close to finding out what the problem is.
Like I said, I'm at the guessing stage now.