I used an insecticidal soap that was marketed as organic from one of the local hardware stores. In reading up on mites, the references I found said products that worked by suffocation tended to be more effective. Because of the short generation time of the mites, they rapidly develop immunity to miticides so if one does go this route more than one formulation may be required.
I sprayed mine down weekly (thoroughly drenching the top and turning it upside down to coat the bottom). I think it took 6 or 7 applications to get rid of the mites. I could see how this might not be doable in a large collection. The soap also caused brown spotting on the flowers, but getting rid of the mites was my priority.
I saw a few mites several weeks after I stopped treatment, but I'm not sure if they were tied to the original infestation. In the mean time, my Dendrobium had also become home to various predatory mites, thrips, and other insects that occupy my yard and I've seen no signs of spider mites for several months now.