OK... Welcome to the site. Seems like you know what you are doing pretty much and have done things by the manual. The first step, like always is to get your battery LOAD TESTED or use a hydrometer to determine if any cells are bad or marginal. A hydrometer looks like an eyedropper with colored balls in the clear part. You put a small hose on the snout of the hydrometer and pull in a bit of fluid from each cell in turn. When you draw in the fluid, if any of the balls don't float, the cell is marginal; that is, partly sulfated and isn't capable of holding a full charge. If none of the balls float, the cell is dead. If you find this condition with the battery, buy a new battery and charge on a low-amp trickle charger for 12 hours... don't charge with a car charger! OK battery is good...
You have checked stator voltages and you are getting plenty of AC. With a new reg/rec combo, you should be in good shape but are not. This means that either the reg/rec isn't getting output feedback it needs, the reg/rec is bad or the connections to the reg/rec are bad.
On the 78, I think there is a PATCH PANEL arrangement. Disconnect the big plugs... the blue is one of the critical plugs. You can check continuity of the pins. For instance, the blue female part connects to the green. Check to see if you can find all three legs of the AC wires as they go to the green plug on its female side. Clean all these connectors. Use spray contact cleaner which you can find at an autoparts or computer store and dab dielectric grease on the connectors. The reg/rec needs to plug into the green wiring in some fashion... let's look at the reg/rec.
The reg/rec relies on a DC voltage sense to set the output voltage that goes to the battery and main fuse. It gets that sense off the very wire the power goes out on for most of the newer reg/rec units. It is critical that the WHITE output wire have a good connection with the tee it plugs into and the legs of the tee are solidly connected. I would consider using NEW wire and connectors if you have an ongoing issue with charging. Probably will be white and white/red 12 ga wire on your bike. These will be the wires that go from the reg/rec to the tee connector to the battery via the solenoid lug and to the main fuse box. Try cleaning them FIRST and dabbing with dielectric grease but if that doesn't work, replace this wiring. If your bike has had issues on a continuing basis, there could be a basic problem with this wiring. On older regulator type bikes, there was a connection from the regulator to the switched voltage source from the wiring harness via a brown wire. If your new reg/rec has a BROWN wire, it uses wiring harness voltage to tell it how to regulate voltage. If this is the case, I would remove the brown wire connection and take the brown wire from the reg/rec and connect to the RED wire back towards your tail piece that is switched DC voltage that runs your tail light running light. The tail light running light is the ONLY thing on this circuit as you MAY have a bad connection in the much more complicated brown switched subcircuit.
