IMO you should be able to shoot sea salt at the butt of any owner who sees a sign and then does or continues to do the exact opposite.
We have footpaths frinkin everywhere but only two main ones that are not fenced around - one runs right through the front yard and inbetween our sheds - its the National Coast Path and has thousands of walkers every year in summer we have easily over a hundred every day - with lots of dogs.
I have signs up for dogs but it is surprising the amount of people who take no notice - I gota say though that in the majority, its mostly people who are from other farms or own livestock who dont put a lead on their dogs as they think/know they can trust them. I always mention that even though they may know their pet - its about setting an example to others - I wouldn't take my dog through their yard without a lead and I expect the same. I dont think this is unreasonable.
Mind you my doggies have never had a collar or been walked anywhere with a lead - so I just wouldnt take them to someone elses farm for a walk

Baz