You'd probably have to put the entire dish through the opening to have it on top of the roof to get it to work. Using a 84101 zipcode, the receiver shows a 163° Azimuth for the 110 sat and 177° for the 119 sat. The elevation of the two is very close there - 42° and 43°. So it is trying to get signal from two places that are 14° different Az. It can do that if the dish pan is right in the opening, but that puts the LNB on top of the roof. The farther you drop the dish pan from that 20x15 opening (if that is feet and not inches, it should work now), the less likely you will still be able to see both locations. What you described "sounds" like you think the signal is coming down from where the LNB arm is pointed. It is actually getting 110 from 7° to one side of the arm and getting 119 from 7° to the other side of the arm. To see both "from the floor" that is 8' from the aluminum roof, the opening needs to be about 27" wide. Even that is just so that each half of the dish sees "its own" birds. You really need both birds to hit most of the surface area of the dish. Are you mounting this on a pole so it is as close as you can get to this opening in the roof? About ever foot you come down from the roof means the dish needs to be moved a foot away from the opening (if it were a 45° elevation instead of 42.5°).
I'd extend the receiver coax outside the patio area - say on top of a picnic table where you get a good signal. Then take a piece of metal with a 20x15 hole in it and see where you can put the metal that doesn't knock out the signal. Or just leave the dish mounted outside the patio! It would be far easier than what you are attempting. I'm with whatchel1 - I don't think you'll find the "perfect place".