Bath tub Drain

OK here it goes. I wanted to replace the whole bath drain. The old twist and turn plug has been broken since we moved in. So I took my plyers put them in the drain and started to twist. SNAP. The bootm part of the drain just broke. Now I have basicaly a rotting metal sleeve with nothing to grip. I tried a pair of channel locks. Hoping I could open them against the wall of the sleeve and turn. No go. It.s PVC piping and I am afraid to use heat or anything that might damage the threads. If I get it out and put anything ba in it doesn't help. Short of having the tub removed and a new overflow drain section out in, does anyone have any ideas?