Yup, you do need some shade for orchids to grow outdoors in summer in FL. Mine are nearly all outside but in the pool cage, about 20% shaded. They can still get sunburn through the screen. So I have two big tall Brugs that are on wheels that shade the sun loving orchids through the middle of the day. They take the summer temperatures pretty well, it's the strong sun that hurts them. Or too much rain!
The 'quarantine' area is outside the cage, but under the big oak tree's canopy. Sometimes the ones out there do better than the ones in the cage - go figure! I treat then banish any plants that show signs of insects or black fungus to prevent it spreading to the rest of the orchids. I have about 100 orchids now, it's a true addiction!
If you have to keep them indoors, how about a guest bedroom that doesn't get used much? Turn off the a/c vent in there, and put them near the window? They really don't like cool, dry air. If you can't do that, what about hanging them on the lower branches of your plumerias? I'm thinking any orchid will do better with heat and high humidity vs. cool, but low humidity like in the house in summer.
Here are my orchid areas in the pool cage - first shelf unit with a little temporary 'umbrella' over it against the 3in. of rain we got yesterday - and more expected today! The other shelf units are under the roof overhang so they get a little spray but not the pouring rain, and morning sunlight. At this time of year, I pull out the roller shade at about 11am to keep them cooler, see 3rd pic. Come about mid-August I won't have to do that any more.