Ugh, I can't help OP but I really sympathise. We lived with my MIL for a little while, and she used to put a lot of food out for the birds, but at GROUND LEVEL. The cottage was on farmland, so although I saw no rats there were constant mice and cluster flies in the house.
We managed to keep the mice away from our part of the house by setting traps and having NO food sources available, but they travelled around under the floorboards and rummaged about occasionally.
Eventually the numbers increased enough that we ended up with a regular mouse visitor - he became so blatant that even our rat terrier just stared at it as it sauntered around the room, and I nicknamed him Kevin.
Thank fuck we've moved out now, I was absolutely sick of them and their bloody droppings. One died under the floorboards once and we couldn't get to it - the stink was there for 3 weeks, it was grim.
I have no solution, but good luck. Try appealing to their better nature, if they have one - it is food that attracts the rodents, not ground cover. Well, not really.