There are times when you just have to go the extra mile. I'd ask my neighbors normally, however if they're really jerks, then I'd just go ahead and do what I had to do, which is below.
1. Go online and find some who sells Termidor. Its a termiticide that is based on the standard Fipronil in dog collars, and is just slightly weaker than the dog collar formula.
2. Get a $15 2 gallon portable sprayer from Lowes/HD.
3. Mix up a batch, and give a nice good soaking to the entire fence line, and your yard. And definately find a time when they are away from home and spray as much over on their side of the fence as possible.
I've been doing this twice a year in my area, as we have foxes, possums, and all sorts of misc. critters in the hills here, even though its semi-suburbia.
I sprayed last maybe 4-5 month ago, and haven't seen a thing except the occasional spider, which are actually difficult to kill because of their anatomy, and even they take a significant hit.
The best thing is, Fipronil is very minimally impacting on mammals, and even less so at the lower levels in Termidor. Plus once it dries, its basically inert to pets/humans.
There is a Do my own pest control website where it is very cheap, however I don't know if I can name the site here. I also have some Bifenthrin, which is just a Pyrthrin, which I add, which may also be helping.
I think for $50 you can totally eliminate your yard pest problems within a week or less.
I know have chickens and a chicken tractor, so I have to figure out how to keep a zone -with-pests so they can get some additional protein.
I know a lot of people get a little freaky when it comes to chemicals, and rightly so. I've done tons of research, and the science has been done and is easily found.
On the flip side, a lot of people still feed their dogs garlic, which is considered a poison due to its thiosulfate components, which are 5x stronger than in onions.
HTH
And if you want a more organic solution, start growing peppermint and geraniums along your shared fence. It just may take a while longer to get under control.
Whoops, just noticed you do spray your lawn already. Spray his too!
And, FWIW with everyone suggesting Lowes/HD chemicals like Bayers, which I also bought.
They are mostly 99% water, with 1-2% actual ingredients.
For about $30-40, you can buy 1-2 pints of the active ingredients, and make 30-40 of the $10 bottles they sell at the store. Nice once you realize you need to spray again 4 weeks later, or your local variety of bugs seem to be super-bugs.
I don't mean to sound rude, but when I read that you had found ONE tick I nearly laughed

! Our nexed door neighbors yard had been infested with HUNDREDS of tick until late last year and was filled a foot deep in some places 4 feet in others of 20 years of leaves and crap! When I just had one sheltie, F-kap, I would spend countless hours, and thousands of dollars to try and kill them all. Can you imagine a dog covered in about 100 tick, the owner spending all day killing them, and the next day they have almost just as many? That's what I did almost every day in the summer. But do you think the people next door cared that they were killing my dog? NO

! One of there dead trees fell on my roof right on my bed room and as it rolled off it fell onto the dog house that had F-kap and Jody inside (Jody was a pup then), luckily the fence and my window took the brunt of the blow and it only left a dent in dog's tin roof. Since then they have paid some one to fix up there yard a little and cut down the other trees (because heaven forbid they clean up there own mess!) but even though it's been almost a year the new fence still isn't up all the way (to much crap in the yard, can't get the post hole digger in). Since then the ticks have gotten a little better, only if I continue with the constant buying of poison.
ANYWAYS, now that I've stepped off my soap box

...
I use Frontline Plus for the dogs,
http://www.frontline.com/Pages/default.aspx
Bayer Insect Killer for the yard, and
http://www.bayeradvanced.com/insects-pests/products/complete-brand-insect-killer-for-soil-turf
Enforcer Flea Killer for the house
http://www.enforcer.com/products/flea-tick/flea-killer-for-carpets/
I hope this helped!

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