How old is it? Any chance it’s corrosion on the threads? Any signs of it?

I ask because an old trick for “seized” threads is actually to try TIGHTENING first...just a cinch, then loosen. It’s a good trick that will BREAK the corrosion bond. Always worth a try. But it sounds to me you’re just having a gripping problem? So, yeah..you just need more surface tension.

Good way for the wood is to cut a 3” section of 4x4. Mark and drill the center of the wood block to the approximate diameter of the break, (or barrel if that is what you are gripping). Then cut the block in half. Sand the two halves for a perfect fit. Works good & on the cheap.