You say that there's a difference between the Limited and the Sport Edition regarding the tire pressure monitor ?
I don't think so. I have the Sport edition with sensors inside the wheels and the computer reports the exact pressure of the tires all the way (I checked with an electronic gage). You do have to buy the "driver's convenience group" with the Sport edition because it doesn't come with it by default (Not sure about the Limited Edition). But it is the exact same thing as the Limited version of the package.
Unless I misunderstood you, my belief is that the tire pressure monitor in the Limited or Sport package of the Compass is exactly the same.
2007 Jeep Compass Sport 4x4
Steel Blue, 26E, CVT, Boston Acoustics, Sec. grp.
Heated seats, Driver's convenience grp.