I have straightened just about every stave I ever worked on to some degree. I use a vise with a swivel base and a post on the end of my work bench. I rotate the vise to an angle that when I tighten the jaws it forces the stave against the post.
I use a piece aluminum angle for a heat reflector and wrap the heated place and the angle with a tee shirt to deep soak the heated piece. It may take 1/2 hour to cool because the angle retains so much heat. I suspect some bending failures are because the heat doesn't get deeply into the wood. There is no doubt about the heat transfer with my setup.
I would go for the dogleg first and not all at one time, I tweak limbs a little at a time to see how they come out. You can get some of it out and bend the handle to finish the alignment, each correction stave to stave is different, it is never one size fits all.
My straightening setup;