Mark,
Mulberry acts a lot like osage, but I don't remember ever bending a mulberry bow. I had access to so much mulberry that I only used staves that didn't need straightening or untwisting. Everything else we burned in our fireplace insert. I was a new bowyer back then too.
I heat bend using that setup all the time (but not with steam). I have 2 suggestions. If you have a long area to untwist, do it in 2 or 3 heatings with shorter sections so you don't have to work with so much bow in the air. I think a form or caul might be a better choice when you have a long bend/untwist to do and want to do it in one shot. And second, if you can, go a little closer to your final dimensions before bending it. It'll be a lot easier for you. I know with dry heat it takes a lot of heating to bend a bow as thick as yours is in the center.
Good luck,
George