Manny, a fellow knot tying friend out in California, sent me a photo of a turks head knot that he tied, being used as a jug/bottle sling. So I gave it a try.
The knot is a simple 3 Lead 5 Bight turks head knot, tied from a doubled up single strand of paracord. You start from the center, treating the cords as one, making a single pass. When you get back around to the starting bight, you run the paracord ends through the center of the bight you started with. Work the slack out of the knot from the starting point to tighten the knot up around the bottle neck, and when you pull on the end cords, you'll find it does hold on tight.
I haven't yet tested it out over time with use, but it does look like a usable alternative to a regular jug/bottle sling knot. I used a 10 foot length of paracord for enough extra to make an adjustable shoulder strap with the ends knotted together.
*Manny suggested using a cord lock on the strands, slid up against the knot to further secure it.