Hey Vic, this problem has been haunting Kzrider since the earliest days. You may have seen the posts on it. (along with the 3-phase conversion info).
To summarize:
Basically, what it comes to is that some of the 78 and 79 Kz650's had charging systems that were a bit weaker than others. Not all of them though. And they were ok with the stock electrical system. The 60-65 VAC open load test confirms the slight weakness. It really should have been closer to 70 or even 75 VAC.
When a Dyna III or Dyna S ignition gets installed, the slight weakness in the charging system results in a slow average drain on the battery when running. Even if it seems to charge initially or at some times, with heat and over time, the alternator just seems to not quite keep up with the load. It doesn't seem to matter what regulator/rectifier is used. The Dyna III and Dyna S have a much longer dwell so they use much more average current than the stock points. If you are running 3 ohm coils, that makes the ignition use even more current. The coil relay mod will likely cause a slight current increase over old wiring given the same Dyna ignition and coils setup.
The solution has been to use a 3-phase stator from a later Kz650 or Kz750four... or aftermarket 3-phase stator. And of course to then go to a 3-phase reg/rec. Luckily, you can get a used, but much newer. 3-phase Kawasaki factory reg/rec for about $10 from a 2000's Ninja. Martin and I have been using them for some time. And of course you can install one of the newer series-pass Shindengen reg/recs, but they cost a bit more.
Since I know you are meticulous, I was hoping you could do a quick analysis of your rotor while you are troubleshooting this problem. Because it's been an issue for so long, I've always tried to come up with ideas why it's some 78 and 79 Kz650's but not all of them.
My most recent thought was about the magnets in the rotor. I think the 78 and 79 Kz650's were the first to get the cup-shaped magnetic rotor/flywheel. The cup keeps them from flying out. In the cup are 4 magnet sections. Each with multiple poles. I believe the magnets can get installed backward. If one is backward, it would reduce charging power by some percentage, but it may still have enough to power for a stock points bike.
I believe this may have been an issue and it's what caused Kawasaki to re-engineer the cup-shaped rotor with 3 magnet sections (instead of 4) on later bikes including the 550's and some/all 750fours. With the 3-magnet section type, the magnet section can be installed in either way and the poles still line up appropriately.
If you have the time and feel up to it, I'd like to know if one of your rotor magnets might be backward. To find out you just run a small magnet along the inside of the rotor and count how many times it flips as it passes over the multiple poles. There will be a pattern to how the magnet flips.
I will post a diagram and video when I get a chance. They will better illustrate what I'm talking about.
If it turns out the rotor has a magnet reversed (again, it's just a guess on my part) then a new rotor would probably be on the menu as well.
Coincidentally, user moroboshi1196 has a bad stator and I'm talking him through the 3-phase solution currently as well.
kzrider.com/forum/4-electrical/610736-bad-stator