I had my car cleaned, and I think they used ArmorAll on the screen (that displays the NAV, climate controls, etc). I think it made this screen even worse in sunlight, and it's always been pretty bad. Anything I can do to restore it to where the surface is only as bad as when I bought it?
you can use some rubbing alcohol to clean off the armor all. But you won't be able to bring it back to when it was crappy and new
First car I ever bought new was a Mazda 323, and the first service visit I ever took it in for, they Armor-All'd everything in sight including the steering wheel. Mazda had somehow worked out how to make that steering wheel with just the perfect amount of tacky-grippy feeling. I really enjoyed it for those first weeks, and then never again.
Don't do that again. You got off lucky; besides relieving you of money and messing up you're screen, you're lucky they didn't run down your 12 volt and/or sprayed water into sensitive electronics. Pressure washing the engine bay, same story: just don't.