How about a DIY route by making a tire scraper mounted to the seat stays? Use a old milk jug or some other sturdy plastic cut to fill the space between the seat stays. Put a notch (with some gap obviously) in it to slide down around the tire. Zip tie it in place and go.
The milk jug plastic probably won't hold up by itself (but maybe layers or a zip tie running between the stays for a brace), but it is a starting point (or a good template). Plastic may get too brittle when cold, but you could try some cheap washable plastic plates (dollar store fine dining, not the throw away kind). Maybe those "for sale" signs (paint it or turn it around face down, don't want to get bugged). Just about any flat piece of it that will lay on the stays, and easy to shape.
I thought about a metal solution but I'm not a fan of sharp edges, and it may weigh more. I'm not a metal worker so I couldn't tell you if filing would work well enough. An old license plate (with painted numbers instead of raised), some discarded duct work, cookie/popcorn gift tin (ah, they do have a purpose!).
Make a note how far the wheel comes up the seat stays (mark with some painters tape), then take it off. Take some heavy paper and template it out. Shape it to lay on the stays without sticking out too far (or fit between them, your choice) and have it go past the wheel mark. Mark out the space the wheel will need. Take it to your material and cut it out, drill out some holes for zip ties, and attach. I bet it wouldn't take more than an hour to get a good enough solution.
This is a close idea to what I'm thinking. Here is a photo search of the bridge between the blades of a front suspension fork. In these the tire is really close to it. Now imagine creating this and putting on the back tire.