UPDATE. The window screen placed behind the box fan works. I had a small bowl of water behind it for a time. But it evaporated. So IDK how many mosquitoes were lured by it. But there are a lot of mosquitoes stuck dead on the screen.
Apparently they are very weak fliers and if close enough will get sucked in. The window screen (held in place by magnets on the metal frame) traps them. Few if any mosquitoes in the greenhouse any more!
I gave in and sprayed Cutter Backyard Bug Spray in the yard. The mosquitoes were just too numerous. It was impossible to work outside of the greenhouse. It's better, now. It works great. I guess better to have chemicals on my yard surfaces than on my skin?? I also sprayed into the forest about 8 feet. Who knows if there is standing water back there? It is too dense with sticker vines to tell.