You say you have about 1 1/4" clearance to your overhead door. With measurements that close, be very VERY cautious about backing in. When you measure your RV sitting unhitched and it's 12'3" (example) and you hitch it to your truck and it sits 4" higher because of the angle of the hitch but the truck "squats" 3" from the pin weight, It's tough to know exactly where the A/C shroud would be backing through that door. If you are measuring as close as 1 1/4", I'd have someone on a ladder watching as I backed in.... All it would take is a slight dip in the drive, a hitch change, even a load configuration change to take up that small of a clearance. Close (very close) monitoring as you back in will prevent a potential "mess"
As for low profile vs standard AC shroud heights, according to the Dometic website, the Briskair 2 is 12 7/8" tall and the Penguin 2 is 9 1/2" tall.