Out of curiosity why do you prefer the heavier profile for a GP rifle?
Based on what I've learned so far, other than weight savings, it seems like a heavier profile is "better" in every way than a light profile. For a relatively short barrel (14.5" in this case), I don't mind the weight penalty for a GP rifle.
If I anticipate lugging THAT particular rifle around all day long, I'd likely choose the SLW over the A1 (if selecting between the two you're looking at).
For me, if I'm looking at a lightweight barrel, then I want everything else as lightweight as possible: lightest rail, lightest optic, flashlight, buttstock, etc. If I'm not going full-lightweight, then I'd rather "save weight" somewhere other than the barrel (i.e. the handguard, light, etc., if I want to cut down on front-end weight).
In my anecdotal experience, I also really like the accuracy of my SOCOM barrel compared to other barrels I've shot.
For what it's worth, when considering taking one of Buck Doyle's scoped carbine classes, I have thought long and hard on whether I'd bring a SOCOM barrel to a course like that (not sure I would given the choice).