Mark,
Adult Norway rats will often exhibit neophobic behavior towards new items or new 'foods' that appear suddenly in their environment, and will even avoid existing items that have been moved or displaced. In my opinion, the act of you capturing a rat at a given location should not cause others to avoid that area for that reason.
I commonly experience cannibalism of captured rats and will reset the same locations, and catch others, but those 'cannibals' could be stressed by limited food resources, high population / competition, etc. at those specific sites. Rats also require water daily - might be a location tip for you - or you could start watering them. Yes they will travel some of the same pathways / edges regularly. If you are blind setting consider smaller footholds vs. traditional rat traps - don't need to be bedded, covered or blended like a coyote set of course, but don't make it a barrier that is easier to go around rather than over, especially with their neophobic tendencies. Could also consider fencing them towards the trap / edge with some wing boards if plausible. I love the 2 1/2" round body-grips for burrow entrances, if you have any of those. Rats 'imprint' on available food sources from the time they are nursing, and from other rats droppings, so if you know what they are feeding on, you might avert some of that neophobic behavior with the right bait. Other than that, due to the periodic nature of your infestations, I would suggest installing your bait ( snap-trap ) boxes in your preferred locations and leaving them there permanently if possible - nail them down, then set up as needed. As far as baits, I use them all, peanut butter, commercial baits, and so on, but my change up baits are Slim-Jim sticks and Jameson's Fireball paste bait - designed for coons I believe, but a truly outstanding rodent bait I have found. I'm no rat expert, but do have to deal with them frequently for my clients. Just my opinion & limited personal experience FWIW.
Good luck & best regards,
Mike Tucker
Edited : And yes, that last one really can be more difficult than a coyote….seriously…. :-)