The ''hole'' problem

On many Lp's from the 80's I have notices that the hole in the center of the LP is very ragged and frequently undersized. I have just had a wretched time getting one of these off my turntable.

Any tricks to clean these up. I am assuming that concentricity is important, or I would just use a reamer, but a reamer is probably the best answer. A nice tool that would fit on the record vaccuum would sure be convenient.