I went from 25c Gatorskins to 23c Vittorias and started rubbing on the front fork on my Bianchi. So I took a dremel to it - worked great, no more squeaking sounds. It looked like someone had aready done that before, too.

Looking at your pics, it looks like you don't have the rear wheel all the way back in the dropouts - the further back that they are, the more clearance that you'll have... Of course, less gear ratio options...