So the problem remains. Strange - initially this had all the hallmarks of a bike that had been jump started from a running car, but not in your ownership we understand, so we have to look at the RR/wiring loom & battery.
I attach an install walk through, for fitting a MOSFET to a Honda (couldn't find a BMW installation).
http://www.speedzilla.com/forums/ho...ngen-fh012aa-regulator-rectifier-install.html
You say the OE BMW plugs have been removed, so presumably the wires from the MOSFET have been spliced into the loom - surely this is where the problem lies? Solder joints can crack up, crimps corrode - somehow you have a significant voltage drop between RR & battery. Then the RR output is over spec (should be c14.5V) suggesting that is failing . Also, if under/overcharging has been going on, the battery condition always becomes questionable - can you beg/borrow a known good battery from a buddy?
Finally, I do not know how the canbus may try to interfere with the output - you would need expert opinion there. However, there is the option to take the DC output direct to the battery as explained in the link.
Perhaps you can post some pics of the connectors & how they are spliced into the loom. Also a pic of the back of the MOSFET RR, the side that is hidden when mounted - is it clean, or showing any signs of overheating. Does it show the RR spec?
Good luck sorting the issue ..............
KEN