I have no experience with heat treating or correcting sassafras, but none of those bends are extreme. If that was just about any white wood I know, I could clamp the whole bow flat and straight to a hardwood 1x2, with maybe 4 c-clamps, and correct the handle, twist and tip alignment all at once with dry heat. Nothing i can see requires steam or any really hard cranking.
If someone can confirm that sassafras responds to heat, that's my advice. I can handle all kinds of side to side wags, but I really like a pretty symmetrical view from the side of the limbs while tillering. The twists and rollercoaster waves don't cause issues with bending and can be worked around, but they sure mess with my eye, creating the impression of fat spots or flats, and making the bow look totally different when viewed from one side, then the other.
Since this is your first.... It looks like a great start, so good luck.