I think you made a great first effort. I agree the setup of the cutters requires a lot of trial and error to ensure the pieces fit as designed. Having a router lift and fence with micro-adjust capability makes the job a lot easier. I made all of the stile and rail cuts in one pass. I didn't have any problems with the amount of material removed, but I was taking my time. When I cut the panels, I made three passes and increased the height of the cutter for each pass.
I kept samples of the stile, rail, and panel from my first project after the cutter height and fence settings were where I wanted them. I used these to set up the router height and fence the next time I needed to make more doors using the same profile. Sadly, they were tossed in a massive offcut cleanout when I had some help last year.
I don't have a lot of experience with building these types of doors, yet, but will later this year. What I have learned is having a matched set of cutters is important. You wrote "a cheapo set from Amazon", and I think that might contribute to some of the problems you described and documented with the photos. The matched set of cutters you bought might not really be as matched as the vendor states. By contrast, the Freud cutters I used produced precise mating surfaces, but I expected this based on the price.
When cutting the ends of the stiles, I use a coping sled and a sacrificial backer board. The stile is clamped in place and is essentially along for the ride and will not stray. The tearout is eliminated by the backer board.
I have the AUKTools 2400W router with the speed control on the NVR switch box. The published speed range is 10K to 22K RPM, so I am taking a leap of faith in assuming the speed control is linear along the range of rotation of the control knob. When I'm using the large panel cutter, I use the lowest speed, which I hope is really 10K RPM. When I'm using the rail and stile cutters, I set the speed control at about the one-third point of the range. The maximum speed for the stile and rail cutters is 16K RPM, and so far they are still pristine and I haven't seen any burning on the wood.