Water in the oil will manifest itself as milky oil, as evidenced on the dipstick. If instead you are only seeing water/oil mixture on the underside of the oil cap, that is a condensation problem, but not water 'in' the oil.

What causes this? poor ventilation OR engine not getting hot enough (less than 160F degrees) OR short, small driving trips (less than 15 minutes at a time). The engine needs to be hot enough to burn off the natural water condensation that occurs.

A modified carburetor does not normally cause this. Water doesn't run through the carburetor, neither does the crankcase breather except at wide open throttle.

Your breather setup sounds like a fairly typical "shade tree" or "backyard" solution, I've seen it done before. I would refit the stock breather system as it won't hurt HP, but will ensure effective crankcase breathing. An old wives tale is that it will hurt performance, but that it untrue. Guys that say that always point to pet theories, but never to any testing either dyno testing or otherwise. Refit the PCV so that the crankcase is positively aired out.

Only if you are racing and the racing rules require a catch can -- only then should the PCV system not be used.