There's not much on the stbd side that can cause this. As I've said before, it sounds a lot like an exhaust tube problem. I know you said the tube feels solid, but if you've already started drilling test holes from the inside, I'd suggest sampling the core around the exhaust tube.
The only other through-hulls to stbd that I can remember are:
Engine cooling water intake
Anchor locker drain
Cockpit drain
Diesel tank vent (but I'd think it's too high to be a problem)
Taking core samples near these might be helpful if it turns out that the exhaust isn't the problem.
Another trick I've seen in assessing core moisture is using a stud finder. Evidently moist core registers higher than dry core. I saw a boat owner at the yard with one, and he demonstrated how he was able to draw a moisture contour around a poorly installed deck hatch, and the contour matched the core samples he took.
If you're located up north, I'd seriously consider checking this now. Once the water in the core freezes, it's going to be difficult to differentiate between wet and dry core.
