Here's what to start tracking this down.
Could be a grounding/ wiring/ voltage drop issue, bad cabling
Could be a bad battery
Could be a bad regulator
There are several issues with these old girls pretty much centered around the ammeter/ bulkhead connector issue, SOME OF WHICH may have been changed on your car
Start by---try a good know battery if possibly and easy to do, I.E. you have another good running vehicle
Otherwise, charge the battery, find someone with a "real" load tester and determine that the battery is A---"up" and B---load tests OK
Next, Get your multimeter and do the following, first with all loads (headlights, heater, etc OFF and again with them ON
With the battery "up" start the car, warm it up, and diddle the throttle (fast idle) to simulate "medium cruise."
Confirm that it is overcharging by stabbing your meter probes directly onto the battery posts, what does it read? If much over 14.5 warm, it's overcharging
Now stab one probe DIRECTLY onto the battery NEG post, the other probe DIRECTLY onto the regulator case mounting. What you are looking for is a VERY low reading, the lower the better, zero is perfect. Anything over about .2V (two TENTHS) is too high. This means that you have a POOR GROUND PATH between the battery POST and the regulator CASE.
So look over your wiring, and add a no10 or larger wire from the regulator mount to the engine block, and recheck the charging voltage, "did it go down" to around 13.5-14.2?
Next, check the "hot" side of the path. One your car some of this may not apply, but you still have a "bulkhead connector". On the older cars, you could have "voltage drop" from the battery--through the bulkhead connector--to the ign switch connector--the switch--the connector again--back OUT the bulkhead connector--and to the regulator ign terminal.
JUST LIKE THE ground path, low voltage here will cause overcharge.
SO just like above, in the grounding test, with the engine running medium cruise, get a probe rigged to the ign terminal of the regulator. If it's accessable, the "run" terminal of your ignition resistor is the same place (used to be blue)
Stab the other probe on the battery hot post. Once more, you do NOT want over 2.v (two tenths)
AFTER you've checked the battery, run these voltage tests, and IF the thing is still overcharging, about the only thing left is an actual defective regulator.
A "new" regulator does not mean "good."