I've been meaning to try an alum block. It's not an antiperspirant, just antimicrobial, but it's literally just a mineral block so there is no plastic container to begin with and it should last a few years if you don't drop it and break it. It costs in the $5-10 range.

The alum still contain aluminum, but not in a form that is absorbed by the skin as in typical antiperspirant, hence why this doesn't prevent sweat; it doesn't block pores. Some people have allergies to the aluminum in AP and some think it is an endocrine disrupter. Other people can get clogged or infected pores from it.