Karen, a swamp-cooler would be of great value to you. Can you tell me the configuration of your greenhouse? I don't quite know that a 15' dome is. Regardless, that make swamp-coolers in all sizes and they are pretty inexpensive. All you need is a water source and a 120V outlet. That would not only greatly increase your day-time humidity but also move air, an important element when growing tropical plants. Could you take a picture of how the deck looks, at least showing the bottom aspect when plants might hang. That's a real possibility there and an automatic watering system could be set up under the deck that would not only water the plants but also raise the humidity. Morning sun is the best sun!
Not only are most of the cattleya a good choice but Vanda are surely a good choice too. Dendrobiums by and large, tolerate heat well, at least for me here in NE Mississippi. Our average high here from June through September is easily 90F (especially July and August) and it is not unusual to have weeks and weeks around 95F. We often see temperatures at or above 100F as well. But the one thing I have that you don't is pretty much constant high humidity.
