So basically what you are saying is that when the engine is running, and the voltage is increasing over the standing no-load voltage of 12.6, then the stator is sending voltage back to the battery (shown by the increasing voltage at idle and higher revs) then the battery is likely at fault for not being able to hold the charge?
That's pretty much exactly it in a nutshell. But for clarification the stator's AC voltage goes right to the reg/rec, where it gets regulated and rectified to DCV, then gets sent out to the bikes peripherals, battery, lights, Ignition, etc.
If the stator wasn't working there would be no AC voltage for the rectifier to convert and the bike would die as soon as the battery reached a level where it couldn't run all the electronics (injectors, coils, lights, etc). If the rectifier crapped the bed, then the system would be getting ACV or NO Volts, which is BAD.
If the regulator was bad, then there would be a constant and acute drain of all battery voltage until the bike stopped running (zero battery voltage), or your test numbers would show a catastrophicly high charging voltage number (+15VDC) while running, which tends to fry everything in the system, especially the battery.
For haha's, check the starter solenoid connector and related stator and reg/rec connectors for scorching or melting. I know you didn't notice any when changing reg rec, but just to make sure.