municycle mudding

I like to be able to ride through mud. However, if I use a Gazz tire, there is only about a 1/4 clearance between the side of the tire and the frame.

Because the mud here is very sticky (especially in my neighborhood) it only takes about 1 or 2 rotations before the wheel locks up.

Currently, I ride a 24"x2.210 tire ($6.96 from Walmart) with 25-30 pounds of pressure. This allowed for a “whopping” 1/2 inch clearance (more at the tread) so I can ride through mud.

While I like the Walmart tire (because it is cheap and I don’t mind abusing it) I would like to be able to ride the Gazz through mud without having to stop, find a stick and make weak attempts at cleaning the tire to proceed.

I noticed that the Kris Holm frame seems to have more clearance (about 1/2") than the Bedford frame I currently ride.

Is there a stock “mudding frame?”
Does anyone have a full 1" clearance from the side of a Gazz 3.0?
Should I settle for a Nokian Gazzaloddi 24 or 26 x 2.6?

(Avoiding mud is not an option)