The stator makes power when magnetic lines of flux cross its wires. The stator doesn't care where these lines originate. In the GL500 it's a permanent magnet. In the SOHC4, its an electromagnet, namely the field coil. The white wire from the alternator drives the field coil. The stock regulator either gives it full battery voltage (balls-to-the-wall), reduced battery voltage (treat things gently), or zero voltage (die-you-bastard-die). These states change the strength of the electromagnet and the amount of lines of magnetic flux the stator windings need to make power. The spinning rotor makes whatever lines of flux that are present, actually cross the stator windings, inducing a developed voltage.
The GL500 R/R has no circuits to drive an electromagnet, let alone control it. I have a CX500 and a manual that covers it AND the GL500, with commensurate wire diagrams. It's R/R keeps the stator from over charging the battery by blocking one of the output phases of the stator. If you wish to prove me wrong, go ahead and try it. But, none of my wire diagrams show any white wire attachment to the GL500 R/R. So, I'm curious how you actually plan to hook it up.
In theory, the CB650 R/R should work. However, I think someone on the forum tried it and it didn't. It likes to have connections to both ends of the field coil's wiring. And, the Cb400 only has connections for one end, the other is connected to frame return. If I recall correctly this confused the Cb650 R/R and it didn't work.
If you want to use car parts, search for Pinhead's posts. He's been promoting a conversion for quite a while.
P.S. And yes TT, the average voltage does drop below 12.8v and counting.
It did this when you jumpered across the black and white wires? (remove the green regulator connection.) If so, your bike's problems are NOT in the V regulator.