Thanks for all your help everyone! While you were all helpful, the winner is....
Someone who has experience creating solutions from problems, and using metal work to come up with truly unique products.
DING DING DING DING
Kurt from Kurts Kustom Firearms!!
You win the gratitude of ME!! And the promise that once the Krime Bill sunsets (with no replacement), you will be asked to turn down my HBAR and install an A2 FS. I even promise not to call you every other day and ask if it's done.
So, what Kurt suggested to me offline, in a discussion about whether a nylon filler would withstand the heat, is to use brass to fill the area between the "convertible" HBAR/LW side sling mount and the LW barrel.
Well, I asked my local True Value Hardware store a hypothetical question. Say I have a clamp that is too big for the tube [er, pipe, I meant] it needs to hold, and the pipe can get to extremely high temperatures, what can I use as a sleeve to fill in the gap?
The suggestion was sleeves that they had in a variety of metals. Bronze, brass and steel. I chose bronze because it was midway (at least that's what he said) between brass and steel in pliability. Not as soft as brass, but more easily bent than steel.
I purchased a 1" long brass sleeve (basically a big hollow cylinder) that was meant to fill the gap between a 5/8" and 3/4" piece. Perfect, I thought. It cost $1.89.
I took it home, hacksawed a cut lenghtwise in the sleeve, and slowly opened it up. I saw that it would be almost a perfect match, but I'd need to cut it shorter and also trim the circumference as it was too long. I eyeballed it and cut a portion off the length and about 60% of the cicumference. Basically I ended up with a part that was shorter and only about 40% of a cylinder. EDITED to add that I filed all the edges smooth.
I took a little work getting that thing down inside the HBAR sized side sling mount, but with a little pushing I got it to fit perfectly. I slid it onto my barrel and drove the pins into the retention plate, using the LW sized "M16A1" side of the plate.
End result is a side sling mount on a LW barrel that has absolutely NO perceptible movement. It is a perfect fit and is firmly held in place.
My description probably doesn't do it justice, but I'll try to get a picture up, and maybe even show the pieces if there is any interest in something like this. A better description of the process with DO's and DON'T maybe, when I get more time to type and think it over.
I can't do much more tonight (my wife wouldn't appreciate being woke up so I can photograph my rifle), but will try to get a photo up tomorrow. Of course, if no one gives a rip, I'll save the effort. Lemme know if anyone else wants a side sling mount on a LW barrel.
In the meantime, here's a pic just to see if my new web pic host works.