I would Gorilla glue it back.
Tap all the ends, and around base, and clamp it down.
How can anyone go into the wood, and extract the broken screws, without adding more damage?
Also, if you try to make an attempt to remove the broken pieces, you are definitely going to have to make the holes (which are trapping the screws) larger than the original hole.
I would glue it, and if that failed, then I would perform major micro surgery.
Secondly, As how this happened?
Heat didn't cause this...
I believe it is highly unlikely that all three screws broken at the same time. I believe they were broken from somebody tightening them too tight, or if they were on too tight, somebody tried to remove and possibly broken just enough to go undetected!
From the closer looks from the breaks, they look to be at different areas. Also, I see no corrosion. The breakage looks sharp and jagged at the ends, and I don't see the broken inner core giving a new sheen, as a fresh break. Those breaks look old.
I would like to take look at the heads of the screws. I would bet, machine was used by someone years ago.
I suspect it was an hidden accident, waiting to happen.
PS...
Oh, wait a minute.... do I see silicon around the screws and on the body of the bass and screws?
Looks like it, maybe this bass had the problem before you knew about it... Hmmmm mmmmm
Good luck.
(Message edited by toma_hawk01 on October 05, 2009)