The best way to deal with it is to work with what the bike wants to do, if possible. fighting it for control results in some very strange reactions. Kinda like it resists what you are trying to do until the sidewall folds the other way, then it "snaps" that direction suddenly...
The front tire blowout is what spooks me. Haven't had that pleasure yet...but a few long distance riders I know have. All were on straight highway cruising when it happened, so it was controllable (to some degree)...obviously if you pop the front while banked over into a turn, you're done for the day...at least...
Punching the wallaby
That's not like "waxing the dolphin" is it? Beacuase you'd get arrested for doing that on the side of the road here...I don't know how the law is down there...