There is no way to seal the entry points from the inside? Honestly I would rather just control the mice than tear up the whole deck if you don't need to otherwise. We have always had a mouse problem too and we're working on sealing entry points but a lot of them are in hard to access locations like yours. We've had a lot of success just with plain old snap traps. The ones we use are these which are nice because you can reuse them but I've heard the old school metal ones work well too. Make sure you're putting the bait (we've used peanut butter) far enough back that they won't be able to just eat it without setting the trap off. We've also tried poison but from what I can tell that doesn't really seem to help at all. Anyway if you can preemptively set traps where you know they're getting in, you can probably stop a full-on infestation before it starts.