Alternator and Voltage Regulator Questions

The electrical stuff is hard for me so I am hoping you experts can point me in the right direction. I think these are simple questions!

Quick background. Original single field Alternator and mechanical Voltage regulator in 69 318. Alternator has been out and tested and got 15.1 volt output without a lot of noise etc. So Alternator is good, I think!

I read the exact same 12.7V at the battery at any RPM. Recovers after being turned off a few minutes to 12.9V. Brand new battery.

At the "BATT" connection on the alternator with the engine off I get the same 12.9V and with Running I get the same 12.7V.

Questions:
These equal readings tell me I have a good circuit from the Battery to the Alternator?

The low voltage reading tells me that the Alternator is not sending power to the battery?

The alternator test tells me the Alternator is working correctly?

This tells me the VR is not working?

A VR like this Mopar Performance Voltage Regulators P3690732 would most likely fix my problem?

If it doesn't fix the problem, I can focus on the wiring from the FLD connection to the VR? Or I should just simply replace that with new when I replace the VR?

Thanks for the help!