transom problem

[Bushwacker]

I assume your picture is of the inside of the transom after core was removed? Water will eventually penetrate polyester gelcoat/resin by osmosis and cause blisters. It's not uncommon on older boats in warm climates if left in the water if an epoxy barrier coat is not applied before the antifouling paint. When you pop the blisters, a liquid comes out that's something like you're describing. If your transom core was really soaked, maybe that happened, from the inside! Here's a link to an article on the subject by Don Casey. The fix for a bad case of external blisters is to peel off the gelcoat with a planer until you get to solid glass and then recoat with epoxy. Maybe you could sand yours down till you get to solid glass and then lay in some new glass with epoxy resin before installing a new core.