Ok, so I contacted Apex Machining (the one you see advertised in the booklet that comes with our rifles). They told me that our receiver is the size of the post-2009 DPMS style receivers which is Low Profile.

Per what S&W told me last night, the barrel centerline to rail height measurement is 1.259" and, per Apex Machinging
"August 2009 DPMS changed the height of the top rail on the LR308 upper receiver. To properly match your LR308 upper receiver rail to the full length Apex top rail, determine your rifle's manufacture date.

The distance from the barrel's centerline to the top of the receiver rail on a pre-August 2009 model is 1.313''. On a post August 2009 model the distance is 1.253''."

Furthermore, the gas block rail to barrel centerline is exactly 1.25".

I believe it is LOW PROFILE. I don't think with our receivers you can simply measure the thickness of the top-most part of the rail.