I've had my share of rain rides, one about a month after I got the bike.
Can't say I've ever felt uncomfortable about it (with decent tires on the bike).
Right now my rear tire is pretty well worn, so if there's a chance of rain, there's also the chance I won't be riding. Got a new one waiting to be put on, so after this weekend, if it's raining, and I wanna ride, I'll be riding !!!
I have the Dunlop 491 Elite II. I like it because it has a continuos channel around it for evacuating water. Plus I like the raised white letters.
As for a wider tire, the widest that'll fit the rear of the Vulcan is the 170 series, but I don't think that'll make much difference. Afterall, there's just the tiny contact patch no matter how wide.
Your problem may be with the power the bike has. It is one of the quickest in it's class. Maybe you just need to be a little softer on the throttle?