You may have more than one issue going on here.
"AC Output test: Please interpret these results: When generator is running 115 volts steady reading no problem. Then the voltage meter pegs zero (within one second) at the beginning of the engine stall sequence. Conversely if I stop the engine with the stop button the voltage drops slowly to zero as the engine dies."
This is indicating that there is a breakdown in the output side of the system. Very possibly a voltage regulator going bad.
If the set quits producing electricity, it will shut the set down, as some of this electricity feeds the coil and fuel pump.
But the one that is really confusing:
"Ignition module test results- did this test for at least three revolutions and the voltage stayed constant throughout the test, it never dropped below 12V."
This is telling me that the ignition module is not operating properly.
But if it is not, the set should not be running at all.
Please do this check for me and let me know the results.
First, remove the (2) 5/16" screws that secure the ignition module to the top of the generator housing, being very careful not to drop the screws inside. If they fall in, the generator MUST be pulled to remove them. They will do a lot of damage if the set is started with them inside.
There is a trick to getting the module out. The flywheel has fins on it to move cooling air across the generator. One of these fins is shorter than the others. The engine must be rotated so this shorter fin is at the top of the flywheel. Depending on how your set is mounted, it can be very difficult to see down in there, and I often have to use a small flashlight and inspection mirror.
Once this short fin is at the top of the flywheel, the module can be removed. It is a very tight fit, but it will come out. Pay strict attention to how the wires are routed in relation to the module. If the wires are not reinstalled EXACTLY as they are, either the module will not fit when putting it back in, or the wires will be hanging in the way of the flywheel and will get cut.
Once the module is out, simply disconnect the 2 wires from the coil.
After the module is out, we need to inspect the ignition rotor for damage. The rotor is a long piece of plastic that snaps onto the crankshaft, and has a magnet at each end. The magnets are what open and close the contacts in the module.
Looking down into the hole, turn the engine so one of the ‘arms' of the module is straight up. Stick your finger down into the hole, and press sideways (rotational) with about the same amount of pressure you would need to slide an empty coffee cup across a table. Turn the engine 180 degrees and test the other arm in the same manner.
The arms should not move. If they do, the rotor is cracked and must be replaced.
If the rotor is OK, just change the ignition module.
Here is a drawing to help explain the relationship between the module, rotor and crankshaft.