I don't think there's any hope with that frame, those tires, and a traditional full fender like the SKS Longboards or the PDW Full Metals. I have SKS, and although they're not bulky they would probably not work with that little clearance.
Something crazy, thinking out of the box... how about putting those tires on an inexpensive winter frame with adequate clearance? Nothing wrong with N+1 if it's to fill a need not met with your current assortment.
I really love riding my Synapse, but added the Quick for that reason; to meet some needs that weren't handled by the Synapse alone. The Quick is the bike I put mudgards on, for example.