I also do not like mesh because I do a lot of off-trail and it gets torn up easily. I use low-cut light hikers for this reason. I would rather go ounces heavier and not get filthy and have my shoes last the trip. Do you use gaiters? That at least keeps out the dirt from the top.

Another strategy would be to use a tight weave outer sock so the dirt does not get to the feet. I do not know if any sock would meet that criteria.