First thing to do is, if I'm looking at the back in the second pic, is to take it down to one growth ring. You can hop a ring in the handle if it is rigid enough, but it's ill advised unless there is compelling reason, some other flaw in the stave typically. ]
Then, again not obvious in the pics, get it reduced down to at least near floor tiller stage. It will make your heat straightening go much easier.
Finally, the caul can be as simple as a 2x4 and some chocks or little blocks of wood of various thickess to "pad up" certain areas to bend around with your clamps along the lenght of the bow. This makes the floor tiller more important, as the it's easier to predict a fairly even right and regular bend of the limbs. This will help one "see" and control the final shape during the heat straightening process.
You can correct both profile (from the side where the arrow pass is) and plan view (from the back or belly view) in one pass, or take your time and use lots of little sessions. It's personal preference. It tend to steer less experienced folks towards the former.
Only other advice for heat straighening is take your time. Let your heat soak, using either enough distance or constant motion to avoid any discoloration, at least at first until you get a sense of what you can get away with. I will typically heat an area of say 5" to 7" for at least 5 minutes before I try to move it, and then test with clamp pressure to see if it's softened enought. It's a thing one must develop a "feeling" for by trial and error. If you get in a rush, you might blacken the back ring worst case scenario. I'm speaking from experience here LOL. Don't mean to mislead here, always apply heat from the belly side but with a caul the heat will concentrate between the stave and caul sometimes.
From an experienced pov, you got a very game a viable project on the bench from what I can see.