Harmonic balancer removal?

From the description it sounds like you have damaged the internal threads in the crank snout because the conical nose was too small for the bolt hole. Normally when I use that style of puller I will put a spacer bushing in the hole after the crank bolt comes out. That gives you a solid item to push on the crank snout with. What I would probably do in this case is to put something like a socket in there that can fit around the nose cap and gives you something to push against. Might even be able to use something like a plumbing end cap. Then push on that to get the balancer off. Then you can access the piece that is stuck and might be able to use the pushing ram to stick into it and rock it enough to get it out. The factory puller uses a long unthreaded section to push on the crank inside the threads. I'm guessing you have one like the second image and the green is pointing at the cap? Or is it something else?