I wear my size 13 EE Red Wings. When first looking at a Classic, I was aware of that problem as well. I found that when I ride, I let my boot hang off the side as well.
However, you find this uncomfortable. Someone else (Gasket, I believe) ended up cutting the rear portion off. I don't believe this is necessary. I think the answer is staring us right in the face:
I'm thinking that if you loosen that setscrew with an allen wrench, you can adjust the angle of the shifter. Angle it up so you can fit your toes under the front portion and the rear portion will actually clear the rear of the floor board and can be used with a little more effort. This configuration will allow you to use the front portion like a normal shifter as well. You have choices!
I have yet to do this myself, but have seen another Classic in a dealership that was set up like this. I'll have to get brave and try it.
ATM
P.S. Don't forget to tighten the setscrew again after adjustment.