jwells is, as usual, dead-on with his advice.
The only thing I could add is that I've had to do this a few times on my tele project. I found one of Dan Erlewine's posts very helpful. He shows the exacts steps to doing a drop-fill repair, complete with pictures (and advertisements for his tools :-). I did the trick with the razor-blade scraper and it works great.
stewmac newsletter - drop fill repair