I think it's a never ending battle.
an easier solution than trying to follow after the dog and correct the brown spots is to train your dog to urinate in one place that you reserve for this.
Find an out of the way spot in your yard that you don't have to look at right out your kitchen window. Back corner, other side of the garage. Put down a patch of gravel, or mulch--something that will keep mud down and paws dry. And then teach the dog to go there exclusively.
You may have to take the dog out on a leash a few times and lead them to the spot. When they go there, praise big time. Create some word to go with this. (At our house it's "Go All the Way..." Which was an impromptu variation of "Go Outside" because instead of stopping, I want them to "Go All the Way" around the garage to the side yard.) Now, it's "You want to go outside?" Dog run to the door. I open the door and say "go all the way." They go pee in their spot, then they can play.
Anyway. With a few hours invested into re-training the dog where to pee, I think you'll end up saving thousands of hours in hosing down pee spots and sprinkling grass seed.