I just lost my most cherished Phalaenopsis due to neem damage. I should have learned my lesson from past mistakes using neem on Phals, but I used a weaker than suggested formulation thinking that would minimize any risk. I was wrong and it hurts.
Anyway, I know a lot of folks don't like to use synthetic chemicals (I certainly prefer to avoid them when possible) but a combo of IGR and Avid seems to work flawlessly for me against several different types of mites.
Having said that, I have to presume that Catasetum alliance plants handle neem treatments pretty well? And even if not, it's probably no big deal since they're going to drop their leaves in the fall anyway, right?
Cychnoches cooperi has such gorgeous flower color to it. Looks like it's really happy in your care.