one of those mystical electrical problems
I understand the KLR only puts out about 210 Watts at about 3.5K rpm.
Headlight High beam 65 watts (110+ watts if you have both high and low on at the same time)
tail light 10 watts
heated grips 30 watts (maybe more if they are no name brand)
Misc other electrics 25 watts
So you are going to be demanding somewhere between 130 to 175 watts at 12vdc, you will not get that kind of an output at idle or low rpm.
Did you check your output at 3.5k rpm?
bad Batteries are notorious for burning up stators, and the connections. I know you KLR guys like to get big mileage out of tires and batteries. Have you checked your battery? easy to swap out for another known good battery and check outputs again, no risk of damaging a battery if the stator is wonky.
Let us know how you make out
I don't think anyone would want to lend a regulator, if there is something wrong with your stator it will likely damage the regulator.