Thanks for the suggestions, everyone.
I picked up a .145 D'Addario Prosteel to go with a set of 45, 65, 85, 105 seeing how it was the next most cost effective option from what's in stock at my local L&M. That's just about as thick as I can go due to the type of bridge used on the SR305, but that's about as thick as I'd want to go really.
Getting it in tune was sooo much easier than the B from the Dean Markley Helix SS. In fact, it seems more stable after an hour than the DM B was after a few days. That could be due to what ixlramp was talking about with the exposed core strings causing some funky harmonics.
I think I'll have to take a hair off the nut (that sounds terrible!). It could be in my head, but I swear I can see the most minute sliver of daylight between the groove and the bottom of the string.
It's sounding pretty good so far I've been banging away on it for about an hour now and it sounds the best out of anything that I've ever tried. It's also staying in tune, which the DM set didn't. I have a practice coming up on Sunday so I'll keep banging away on it until tomorrow night. If everything sounds good I'll keep it on. If not, I might try the Chromes. They're pricey as hell around these parts, but they have slightly more tension.