I am new to this forum. I'm an orchid grower since 1972....in a grow room in the basement and a 14' x 18' greenhouse. Many of my plants have received AOS awards...and, currently, my watercolors are appearing monthly in Orchids....the journal of the American Orchid Society. I also grow native orchids and several hybrids of native orchids. I live in northwestern Illinois and have been struggling thru this hot and humid spring/summer...anyone with a good recommendation for a cooling system? Here's an example of my watercolors...more can be seen at marciawhitmore.com.

I don't know about a good cooling system other than moving the Orchids outside for the Summer into a protected spot and cooling them down with a refreshing shower from the faucet unless it rains.
Welcome to the Orchid forum!
Your drawing is wonderful!

Oh, from the Great Lakes area!
You should investigate evaporative coolers or wet walls or wet pads. Basically you run water through a large pad at one end of the greenhouse. A series of fans blow this "water cooled air" from one end of the greenhouse to another.
Pipes recirculate the water up and then down the wall.
I have seen them take 100+ greenhouses and get them close to 80 degrees.