Hey Colin, sorry to hear about the glue withdrawal....
. Kidding of course. 
I have a hunch that steaming with a wet rag against a dent and the flat paddle that comes with some Weller soldering guns might swell small dents through the varnish. I've done this with success if the dents are shallow.
It's place the hot paddle against the rag, wet on the dent, count a few seconds, remove the heat and repeat half a dozen times or so with waiting a minute in between sessions to let some swelling happen.
Since your plan is to remove the neck and refinish anyway what do you have to lose?
Good luck with the withdrawal, I plan of sleeping better tonight too.
