Have you spent time to ensure there aren't piles of stuff on your property? I know you can't do anything about your neighbors or the fields nearby, but the only times I have ever seen mice on my property is when I am doing yard work, create a pile of brush or grass or leaves or something and then leave it for a few days because it started raining or something half way through. They like those piles. I think other things such as bird feeders or certain types of vegetation on your property may attract them. However, I believe that mint will be a deterrent.
Instead of poison, apparently chopping up cork and soaking it in grease from cooked meat will work as mice can't digest cork and it will cause them to die.
http://www.wikihow.com/Get-Rid-of-Rodents-Naturally
Just because you replace the steps, doesn't mean you may be mice free. Maybe a combination of the two?