I don't know how similar your river cane is to bamboo, but I have found that some will heat up go bendy and be OK while some will heat up, go brittle and snap. When I have tested the ones that snap the whole shaft seems brittle, as if it is somehow rotted or something.
I have found I get better results by working on one small section for a small bend correction, putting that shaft down to cool and moving through the whole pile, then picking up each one again and doing another small section. I think this way the whole of the shafts gradually becomes straighter without anyone part being too stressed. In the end a shaft can have a few small kinks and still be an acceptably straight shaft. I found a simply meths burner, as used in some camping stoves (triangia type) gives enough heat to do a nice job without bruing too much.
I think a propane burner can be too hot and too localised. I got lots of breakages when I tried this myself, less with a larger less hot more spread out flame.
I generally hold the shaft in my hands, sight down it and put a gentle bend in with my hands. if near the end I will hold the shaft in my hands and push against a table surface. Localised heat will allow most of the bend to happen where you need it. Lots of little bends seem better than trying for too much at once.
The biggest killer is too much heat. I have found that shoot shafts seem to be alright if scorched but bamboo not so good scorched, maybe because the walls are som thin.
Good luck.
Mark in England