My living room is actually designed very similar to what you have in mind, but in one direction only. You should have no problems.
Now I had an idea for you though. I don't remember where, but I have seen this done before: Run your garage door (assuming you are installing a standard sectional overhead door) diagonally upwards, following the roof rafters so that it disappears above your ceiling leaving you nothing but clear headspace below. You should be able to header off both ends of the opening and have your finished ceiling run to just inches from the wall in that area.
"I've cut the dang thing three times and it's STILL too darn short"
Name withheld to protect the guilty
Stew Hagerty