Honestly, you already know the answer to a mouse problem.
Multiple cats.
I am not trying to be funny. I have a corn field in back of my property. When I was down to one MALE cat, I had mice.
I have 4 female cats and one male cat right now. They are inside/outside kitties.
NO mice in the house, just in the barn, when the horse feed is, and in the loft.
My metal back house door wasn't put in right. The frame has gaps and I can assure you ANY MOUSE can and does get it in. WE just never see them.
Mice will invade you kitchen. They run through your flatware drawers and they have no bladder and carry diseases.
Unless you are inSANELY allergic, I suggest that you pick up a couple of litter mate kittens and raise them up.
I was never a cat person until we got them for this 5 acre property.
Cats can and often are Very affectionate.
Just sayin...