Alright, I couldn't let this one go and it was driving me nuts. I'm not proud of the amount of hours I put into this...so many trial and errors and getting SOOOOO close, but not close enough. I gave up and then went back to the drawing board later and came up with a more 'staged' approach where smaller and smaller engines funnel fuel out of the larger ones. The thought process was based on the fact that I could easily get the apoapsis more than high enough, but never got the periapsis high enough. By staging the rockets TWR, it allowed me to 'coast' farther out so I could stop pushing the AP and start pushing the PE...
Anyway, here's my attempt/success. I had a little too much fuel in the final section and didn't want to cheat the challenge by time warping to stop the rotation, so it's a fairly long video with a few points getting close to throwing the orbit off, but in the end I got a nice stable orbit.
Oh also, the end of the video has most of the important parts of the build shown incase anyone wants to mess with it...weirdly enough, after it worked 1 time, I started recording it, and it failed, then the 3rd attempt it worked again...not sure what was different, but could just be some randomnesses being tossed in...
Sweet challenge, thanks for the idea!!