You are not alone Woodgatherer. I don’t like putting anything in a hive I don’t have to.
I have no experience of the Bee Gym but as mentioned, whilst it may help dislodge some adult of which a proportion then falls through the open mesh floor, does that constitute sufficiently effective control at the colony level? I somehow doubt it.
I think many of us would love it if say, icing sugar dusting proved a viable alternative to commercial alternatives. Problem is there is poor evidence it works well enough unless applied quite invasively (i.e. all bees shaken off frames into a box and communally dusted, then tipped back into the hive). One of the things you pay for with registered medicines is trials having proved they actually work.