MOLES . . . the enemy

I have the same problem in South Fla and have tried EVERY scam you have tried. Bottom line is- the Moles eat the grubs and worms in your yard. Get rid of the food source and they will go next door... until the insecticides (granules or sprays) break down. You need to stay on top of it and reapply religiously. Also- it doesnt help if your neighbor doesnt take care of his yard because they will just hang out next door and look for the right time to return.
People use Dylox but I like Sevin because it kills the grubs as well as over 90% of earthworm population plus who knows what else that the moles feast on.... It's about the nastiest stuff you can buy off the shelf at big box stores. See these links:

http://turf.msu.edu/home-lawn-grub-control-products/

http://www.bayeradvanced.com/insects-pests/products/24-hour-grub-killer-plus

Good luck