Welcome aboard, Sierra!
Sounds like your carbs are close to the condition mine were in when I bought her, minus the cacked sediment (sand) filling the float bowls. You should be able to get her running again with a little elbow grease and a lot of cleaning. You know what works good on carbs? Those cheap toothbrushes you can get at a drugstore! Just remember not to use them on your teeth after using gasoline and solovents on them.
If you can find them, small pipecleaners will work wonders on jets and passages. For the smaller ones, or if you can't find a pipecleaner, you can use a metal twisty tie with the paper covering removed (you know, they come with trash bags to tie them shut?). I suppose regular wire would work as well.
Let me guess which wires are causing you fits when wet, the one's under the seat? In particular, under the left hand sidecover? You could try pulling the connectors apart and applying lithium grease (I think thats it) around them, then reassembling. Other than that, just try not to get water up there and/or cover them with something before washing.