Have you tried talking to your neighbors about this?
So I just caught the main offender on his walk and introduced myself. Said I was trying to catch everyone with dogs on the block and ask them to try to direct off my lawn, since it's in pretty rough shape. His answer was that he thinks it's a sewer issue, and he's been trying to talk to the HOA about it. (yeah. no.)
Anyway, I was clear about the dog thing, so I'm very interested to see if he starts redirecting going forward.
Wait, what? He thinks a sewer is backing up just in the edge of your lawn, and that there have been no other side effects? Yeah, I think he's just in complete denial and a bad neighbor to boot.
I actually think you did the most effective thing to talk to him directly; sounds like he wouldn't have been deterred by a sign.