If considering just a VR swap (good idea), you need to know what kind of alternator it is. Sometimes the no-brand ones seem to purposely clone a Bosch / Denso / Valeo whatever down to the individual part level, so in those cases swapping a Bosch VR into a no-brand (e.g., RTX) Bosch clone would work. But you'd need to check first if it's a clone and that parts are fully interchangeable.
For example, on my 3.0i, the car was shipped with either Bosch or Valeo alternators; the entire alternator can be swapped out for the other type, but at a part-level, nothing at all is interchangeable, not even the pulley.
So never having heard of RTX I did a quick google, and the first two links contained:
"RTX Alternator-Eurocarparts AVOID at all costs!"
RTX Alternator-Eurocarparts AVOID at all costs! - General car chat - E46 Zone Forum
and
"Was it by any chance an RTX alternator? If so, push the boat out and just buy a Bosch, Delphi, or Lucas and it will be reliable."
https://forums.moneysavingexpert.com....php?t=4988246
So you're not the first one with problems like this.
And yes, 16+V is no doubt at all a problem with the VR, which could damage all kinds of other stuff in your car. So get that out of there, and good luck.