You may be able to be a little less agressive by using i) a wet vac first to do as much as you can, then ii) use some alcohol [not to drink, but] to help flow the water out, and iii) then use the wet vac and some modest heat to wick it out.

If the core is deterioted, not just a little wet, then you really need to clean it out from below, re-core, and then glass it back in.