did you EVER replace the chain rings? I see where you said you were told to, then blah blah, and blah blah, and new everything BUT chain rings and.... same symptoms.

a badly worn front small chain ring will be happy to toss your chain off

and it sounds liek you really stand up and power this bike. now, if you're already in the lowest gear and climbing a steep hill, there's not much choice, but otherwise, you should be spinning faster in a lower gear.