i have the exact same bike (albeit w/ gears on it) and i run 700 x 25, which isn't really applicaable your situation.

BUT, the bike was originally sold as a high-end tri bike, so i'd be really surprised if you could get a 700 x 35 0n there.

that being said, i don't think there's any reson you couldn't grind down that washer on the rear brke bridge to give yourself some extra room.

don't remove the bridge itself though.