I'd also suggest you start placing something like them bucket traps that go on top of a 5 gallon bucket,(they sell the lids on Amazon/ebay)
I keep a few about my place, and catch many all yr round in them
I found HOT gluing some bait to the underside of lid, in back where trap floor falls/opens, helps save me time from having to re bait things, as they never get to eat the bait before falling in bucket,
I also add water to bucket in warmer weather, so they drown, but if you do this, you need to check often, before they start to rot in water and smell bad!
But there great traps, IMO and worth there costs,, due to they can catch many mice in one set, over other traps!
I'd suggest placing them near your up near where you park the machine
so maybe you can catch them before they get inside machine and do damage!
I would also try and find out why there are so many near things, is the machine near where you keep feed/seeds or likes??
as the only reason mice normally go to an area is for either food/water , food near by, or safety after eating! so if you can find out WHY there going in your machine and area about it, maybe you can help control them that way too!
there are also a lot of home made poisions that are pet safe, a quick search on youtube or online can show you a bunch that are cheap and easy to make
lastly, adding fresh moth balls in machines, also helps deter them, if removing head liner is a big project, maybe a small hole and throwing some in there could help??
but be aware it could also, become a headache hearing them roll about while using machine, !!
in MY machine, I place bait in places I know they can access but yet, not drag it away, so not to harm other critters by getting it, draw back to this is some times they eat some and die in places that ain't easy to get them out of in machine and they stick for a while!