Might it also be possible to include a check-valve sort of flap that would
allow exhaust but would prevent dirt from the tailwheel from entering the
tail boom?

bumper

I have given it some thought.
Installing a brush wiper at the front and rear to clean the rolling face.
of the wheel. Also a smaller wheel would allow a secondary fender.
The original wheel is about ~7". A 6" wheel would be large enough.
That would allow room for some sort of baffle.
Udo