Once you have a working proof, no matter how bad, you can work towards making it nicer. It's like refactoring in programming.

If your proof is machine checkable, that's even easier.

That is also how humans work mostly. Once every full moon we may get an "intuition" but most of the time we lean on collective knowledge, biases and behavior patterns to take decisions, write and talk.

I haven't had success in getting AI's to output working proofs.

You'd need a completely different post-training and agent stack for that.