... - and will go over 16 volts when I increase RPMs... It sounds feasible to me
Right. Look at a 32a stator. Half the sweep north is 16, and half the sweep south is 16 = 32a. There are 3 parts to the charging system; batt/vr/stator. Stator makes its own E up each wire and that is 16v say is the constant. The vr is the volt changer from AC to DC and regulates the 14v values, where the 1.6v is sent to ground.
Whereas the vr is still in the wiring loop, but 16v passes over/thru the wires and all 16v enter the battery, and that surface 16 heads for the bulbs and blows them out due to so much resistance built into the bulb... filament being a mini fuse and a light source, so a new vr is needed. Then check voltage stability.
Some swap all of it out even with a good stator blowing out bulbs. Again, your bike, your call, but throwing parts at is is one way, and diagnosing individual parts is another. Or said another way, you don't take a suppository for a headache, and you don't take aspirin for constipation. It's either or in other words.
Edit:
Yeah, the AC could backwash and heat the stator on the reverse. But that might take awhile to burn out the stator if there is the 'for every action'...etc. Only your fluke knows for sure if the stator is still serviceable.