Clearly the battery is over charging, I'd try this
Check the regulator is functioning
Back in the distant past I had overcharging problems, in my case it turned out to be the yellow / white wire had broken away from the regulator, I also had blowing headlight bulb at the time though and I note you said that you dont have this other problem.
At some time I've thought a way of testing the regulator is actually doing it's job, though I have never needed to do this in anger.
The test is simply to verify that current is passing through the regulator
If it is, then to me It's working, It's disposing of excess voltage by passing current back to chassis.
Disconnect the regulator yell/whi
Set your multimeter to ac current (20A), not 100% sure on the ac setting though...try dc too
put the meter leads in series with the loom socket and the regulator plug
Start the engine and try different rpm's, you should see varying amounts of current passing through the regulator, if so...then it's doing a job and can be deemed OK
All this can be done without any further expense because you do have a meter.
Like I said, I've thought it but never done it so look forwars to seeing how you get on with this test.