Stubborn toilet seat bracket

Hi everyone. I have a top-fitting toilet seat, and one of the rubber plugs perished and the bolt just came out.

Fine, I thought, I'll just replace the seat. But although one plug was already out, I can't for the life of me remove the second. It's semi-perished, so the bolt doesn't have any purchase, but it's not 'perished enough' to be pulled out.

I've tried WD-40, I've tried gripping and pulling, I've tried leverage... all with no joy and I'm now out of ideas. Can anyone help me out?

Pic attached if it helps.

Cut the head off

If you cut the plastic mount and pull it off, the bolt/fixing will fall through.