The attached .PDF is the new and improved schematic!
The three op amps on the bottom form the current limiter circuit, its basically just a precision clipper with an adjustable upper clipping point and a lower clipping point at 0V. This serves to limit the maximum current of the system to anything up to 10A. Much more elegan than my previous Zener diode solution.
The "fast inner loop" is the current loop, and I formed the slow outer loop with the AD633, three op amps U1A, U3A, and U3B. U4A has the power/current setpoint pot on it and feedback from the calculated power out of U3B. I was noticing a lot of noise at first like you see below:
I then added C1 and R10 and now I get a nice smooth output like this:
With a pulsed input you see the same results, thought made a bit worse when the input switches. I realize that the trick to getting these oscilations to appear was to use the step input voltage, so that the massive voltage spike when the source turns on would trigger the oscillations. Using a pure DC source to power the load in simulation results in no osculations oddly enough. I still need to redo the drawing and make sure everything has a footprint associated with it but for now I think the core circuit is complete. I will also be adding a precision 1V reference, R3 will be switched between the input voltage and the precision 1V reference. With a 1V input power = current so the power feedback control loop will then function as a current feedback based control loop.
Thank you everyone who offered advice! I really appreciate it!