I like your distinction of big bike sport TOURING vs SPORT touring. The whole generic term of "Sport Touring" is overused across too many bikes, so the label mostly loses it's meaning. In terms of the K1600 and GW, I think it's fair to say K1600 = SPORT Touring, and GW = sport TOURING. There are many challenging roads (throughout the US) that will make that distinction clear. But assigning SPORT to any HD touring bike is a reach at best. The big HDs are the ultimate definition of pure touring that is out there.
I'd like to understand where you felt the GTL was lacking on the long ride. Is your bike completely stock, or does it at least have upgrades to the seat and windshield?
I agree that HD is Touring, not really Sport Touring.
Again, this is just my opinion... On my trip I had a Sargent seat and stock windscreen.
The seat is quite hard yet a 700 miles day was fine. You get tired either way, but my butt was not complaining.
I'd say that the screen was the biggest issue.
After the trip I replaced stock with CalSci, but did not take any extended trips with it.
Still, the comfort of MY Wing (which has an upgraded seat, Traxxion suspension and screen) is just there.
I guess if you switch to the GTL after a sport bike or some other smaller bike - GTL is great luxury.
But once you are spoiled by the comfort of the big touring bikes on long rides....
That's why I kept my Wing.
These bikes fill their own niche in my heart

if you know what I mean...