No room for a true glasshouse or maybe not even a shadehouse,then what about and Orchidarium.
Its basically an Aquarium for orchids.
These days with the low heat, low power usage LED lights its so easy
Just buy as large an Aquarium as you can afford for the position and away you go
A six foot aquarium costs only about $200
They may be heated or unheated. They may have a pond in the base for frogs or even a compartment for tropical fish!
I had one as a teenager in my bedroom. It always smelt fresh and foresty and eathy.
There are whole website and forums dedicated to Orchidariums and they are huge in New York, London and Paris as well as Tokyo.
Here's a link to a forum for starters
I do remember the frogs damaged a few plants ,so maybe avoid a big green tree frog.
We have magnificent virgin cork bark that never rots to help decorate as well as all the moss you will need.
A layer of charcoal at the base is a must for a sweet healthy tank.