After brainstorming ideas for how to deal buddhistly with the mice and receiving some good suggestions, I ended up calling my landlord after all.
He didn't hesitate a bit. "The exterminator will be there tomorrow, Johnny."
That's not exactly what I had in mind. But there were some problems with handling it in any other way.
Neither a cat nor a snake would have been allowed in the apartment because of the terms of my lease. Also, given that the plant I finally got around to buying for my apartment is already dying after only a couple weeks of residence on my coffee table, I am wary about accepting responsibility for any other lifeforms. I'm not real ethically wild about the idea of having pets anymore either, though I think it's near indisputable that adopting an abandoned animal from a shelter is a positive thing to do. And the live traps had the potential to become torture devices.
I called the landlord because I concluded that this wasn't my decision to make. It affected people in other apartments and the landlord's property. The dilemma of whether to give someone information when I know that I will not approve of what they will do with it or how they will react to it is one I think about a lot, but I don't have a good answer.
Dealing with this category of problem is also the landlord's responsibility, not mine. That could be a cop-out, but I also think it's unhealthy for me to try to hoard responsibility from others based on the belief that I can handle it more ethically than they can. If I wasn't ready to give the landlord the authority to be responsible for taking care of the building, then I shouldn't have signed the lease.
So I called the landlord, knowing that I was indirectly calling in an air strike, but I think it was the right thing to do. The exterminator came this afternoon while I was at work, and I haven't seen the mice tonight.