rudder pintle

One of the screws holding it in has half come out whilst sailing it yesterday. It's quite loose in the hole - I've tried retightening it, and theres not much 'bite'. Obvious answer is a bigger screw but it goes through the pintle and an alloy plate before going into the wood hull and I don't think theres a lot of clearance for anything a bigger diameter - longer perhaps, but is it likely there will be anymore wood for it to go into screw into beyond the existing 2" screw?

Would drilling it out much bigger, say 1/2", and epoxying a dowel in work?

Doubt theres enough depth at transom to get a useful hatch in. Difference between inner and outer skins there isn't much more than the drain plugs that are in the transom.