I had success desoldering the PGA without damage. I want to thank everybody for their advice and ideas.
The original board has now been socketed and works fine, as does the removed MC68881.
I took a different approach and bought the Hakko FR-301 desoldering tool. A little expensive, but I was amazed how effective it was. I assumed it would only be good for a first pass and then I'd need to do some additional work to get the more stubborn pins out, but the entire chip was loose after the initial attempt with no damage. The pins themselves were also quite clean, I guess thanks to the vacuum strength. I can strongly recommend this tool for PGA removal.
About chip-quik: I had tried reflowing some on to an existing pin as an experiment and it stayed balled up in a blob and did not flow well or integrate into the existing solder. Maybe my technique was wrong, but it didn't seem useful in this application. I understand it's mainly for surface mount work but wanted to judge it for myself. In the end I did not need to use it.