Not an option. Like I said I have a pair of redtail hawks feeding on the dead ones that I leave for them. Although I haven't seen them in about a week, we did hear them twice this week. Sounded like they were on the neighbors roof.
Sounds like time to set up some red flood lights, traps and a baiting station with ding donger. Very interested in what works out for you, and hope no more screens need replacement. Just ordered a pair of red LED flood lights myself, in preparation for when the weather breaks up here.
I was talking with my girlfriend about your rat problem. She suggested that you set a Barn Owl box up high in the area with the problem. She said, Once a barn owl nests in the box the rats will be taken care of in "short order". She's a GRIT magazine subscriber, mensa member and more outdoorsy than 95% of the men I know, so I'd give her suggestion consideration. And no, she's not butch either.
This is the best rat trap I have found so far:https://www.tomcatbrand.com/en-us/products/rats/tomcat-rat-snap-trapBait it with dried apricot (learned this from a pro, far superior to peanut butter). The trigger pad can be set super light. It even ketches those pesky super fast kangaroo mice that can jump out of a trap as it triggers.I have six of these and after a couple weeks no more rats. Seven rats total. Not as fun as shooting but highly effective.