My question is, what sort of a greenhouse do you have and where is it in the
greenhouse?

My greenhouse has a fiberglass covering and faces due south. The plant is
hanging like some of my other cattleya types from hooks about 12 inches below
the interior surface of the greenhouse covering. I have two other mature catts
in bud so I doubt if light is an issue.

I wonder if these plants like a cool drying off period in order to initiate
blooming?

There are no roots outside the pot.