latindane
Learner. EuroPW, NaPS
One could also play with BP, but doing it mid corner is dangerous as it might upset bike suspension and lead to same result of sliding on ones ass.
One way to move weight around without upsetting the bike is keep your butt and legs/feet planted where they are, and move the head/shoulders into the turn. If you've been pretty much straight up with the bike, that will give you a chunk of help.
If, on the other hand, your upper body is already to the inside and you would need to move on the bike (legs/butt/feet) to put more weight on the inside then I agree with you, you might end up upsetting the bike.