Usually you either submit or they roll through. If they roll through you take side control. Why are you trying to untangle and take the back instead of finishing the submission?
Basically it was a suggestion someone made to me. I had uma plata on a guy, he couldn't roll out of it, but he wasn't tapping either. The instructor told me that its so easy to resist uma plata that I should learn how to take the back...It makes sense to me...if the guy's not tapping, i'de rather give up the submission and get the back than have my partner roll out and leave me with side control, wouldn't you?
That's a personal thing I guess. I prefer side mount to back control. It just seems easier to keep the position. If you wanted to go for the back I would say keep the arm lock, keep your arm over their back. Shift your weight into their back and slip your legs free. You would basically have them in a standard turtle position and then work for hooks from there.