Gosh, it sounds like you've done everything you can. Rats will stay around if they have a food source, and their numbers will adjust accordingly. More food, more rats. You have obviously removed food sources from your property. Do your neighbours have compost heaps, bird feeders etc? Is there anywhere else the rats could be feeding?
Shooting with an air rifle sounds quite theraputic. My Data used to shoot crows (I think). They grew to recognise whether or not he had his air rifle and would hang around mocking him when he came out without it, but fly away fast if they saw it in his hands.