Hello Minka Bug,
Well this little issue has reared its head a number of times over the years. Even in the Marines we had the challenge of losing "line of sight" on target areas do to "road dust." So this issue has been on the minds of many for a long time.
Now a little trick you may wish to try before all others...if you are game for it. Is a "manure tea" and "clay dusting." These two methods have served me well over the decades when such an issue arrises.
Secure some rabbit, goat, or sheep droppings, I like these as they are not unpleasant to handle and smell. Horse and Cow will work yet the fiber content is too
course for ease of processing, plus the first forms, especially rabbit and goat are what I make "moss grower" out of. This "tea" needs to be the as strong as you can make it and adding
urine (usually your own is the easiest to get) gives it the final punch. I would suggest spraying (with a pump bug sprayer) at night, as the smell can be a bit "strong" and this little clandestine operation can lead to questions some may not care to field with neighbors. The tea blend is not much different (if at all) from other manure teas used in gardens.
You are going to spray it on every other day and immediately dust the area with a powdered clay. Clay cat litter will often work if need be as most are a bentonite. It will usually take less than two weeks and may never (??) need to be done again depending on soil types and microbiome organisms in your area.
Here is a link to a commercial form:
PolyPavement
We have used this with success, and it has been used by members of the AZA. I don't like having to resort to epoxies or other polymers, yet on some operations it becomes a necessity of time, safety and conservation of vintage materials, so we will use them. They do have to met my criteria of environmentally safe after application...This one has and does thus far.
Good luck...
j