Do cyclocross/interrupter/touring brake levers reduce brake performance?
The only way that interrupter levers could make much of a difference is if the installation requires extra housing (which would compress under braking, increasing the lever travel for a given braking pressure). If you're not bottoming out the levers, though, that's not the source of your problem (and from the picture I don't see why the interrupters would require additional housing anyway).

I think Daniel R Hicks is correct here--your lever/caliper setup likely isn't giving you enough mechanical advantage. You're squeezing the levers as hard as you can, but you're just not getting enough pad/rim force for decent stopping power. You notice this mostly in wet weather because there's less pad/rim friction when they're wet.

Finger positioning on the levers is one thing that can make a difference--keep them as far away from the pivots as you can. On my drop-bar commuter bike, for example, I need to ride in the drops during wet weather because I just don't get enough mechanical advantage with my hands on the hoods.

You might also see better braking performance if you switch to softer brake pads, or rain-specific pads like Kool-Stop Salmon or similar, though I've read that the Salmons tend to chew up rims pretty quickly when it's dry.