Electronic Ign. Control Unit (ECU) Heat condition

2) Checked for voltage at the IGN lead to the Starter relay with key Off and in On position = 0V. (Need to get a helper so I can check when key is fully turned to Start.)
That or a pair of alligator clips, or roll down the window and stick your hand in and turn the key - assuming a column mounted key

3) When car is hot (and turning the key results in nothing at all), the car will CRANK STRONG and start fine if I turn key to On and JUMPER THE Starter relay between the Pos+ post and the square Sol post just under it.
So Run position works and start does not.
Don't know exactly what you are jumpering. Don't know what you have. Don't know if the warning or interlocks are on it.
Best guess is you either providing power to the relay or just direct feeding the starter solenoid.

I am just too ignorant to understand if/how the VR resistance would impact the signal to the starter relay when the key is turned. Does it?
There's other threads on how votlage regulators works. Bottom line is it controls flow to the alternator rotor.
5) Idling Voltage reading taken between the Starter Relay Pos+ post and engine block = 13.9V.
OK. If you are testing for regulation issues, you need to increase throttle and see if voltage follows rpm. If you are looking for voltage drops, then measure at the alternator. Not sure why you're looking at this but it doesn't hurt.
I don't think I mentioned this before, but FYI. The Pos+ lead from my trunk-mounted battery goes directly to my starter.
Pretty typical with batteries in the trunk.
You need to draw a diagram of what you've got and/or post photos.

Starting circuit was not shown in anything posted above. But that is what you need to check out to find the problem.
Schematically this is all that should be involved - although yours may have seatbelt interlock or warning buzzer tied in.
Ignition switch provides power to the relay and a neutral safety switch completes the connection to ground.
The relay then internally connects power to the starter solenoid.
Coil and ECU get power power from the Ignition 2 wire(s).
upload_2019-8-29_15-6-33.png