Thank you for the advice everyone. I have tracked down the issue: It is both the nut and the tuners. The nut is grippy. Strangely so. I'm not sure exactly what the Graph Tech nut is trying to be. If the design goal is to act as a quasi locking nut, a'la Floyd Rose, it fails. Nor does it permit the strings to slide freely.
I purchased Big Bends Nut Sauce & applied it. It helped a little bit. So I applied it again. It helped a little.
SO, I thought "Well, I wonder how the tuners feel when they aren't dragging a string through Mr. Jr. Loctite Graph Tech nut, and they weren't smooth. They too had a grippiness in the mechanism. I can open them up. oil them (I not only have plenty of BB's Nut Sauce, but I also have some pure Silicone oil), but should I have to on a BRAND NEW GUITAR?
Not only is this the only guitar I have with this issue, here's the REAL kicker: I bought an Epiphone Les Paul Standard a month before I bought the Gibson. I liked it, so I figure I'd "upgrade." It also has Grover Tuners, but a different nut material. It too didn't tune all that well. I put the Nut Sauce on the Epiphone (for practice, as it's the cheaper guitar) and it helped quite a bit. Not so on the Gibson.
At this point I have 3 "Les Pauls:" Gibson, Epiphone, Chibson. The Chibson tunes the nicest, the Gibson is the worse. Explain how this is possible? Explain how this makes sense?
So at this point I'm faced with repairs, or whatever, for a brand new guitar that I think shouldn't have problems. I base this on experience. I own many guitars, mostly American, but some foreign. NONE of them have had this issue. I am VERY disappointed. There is no excuse for the premier, arguably the number one guitar company IN THE WORLD to produce anything inferior to anybody. Plus how does it make sense that three guitars, all with Grover tuners, but presumably different build-quality, with Gibson ostensibly the best of the three, to have the worst problems, & the cheap foreign made knock-off to have superior tuning feel & stability?