Lawson glowire works well with lineloc3. I believe that's 2.2 mm.
I used that for my myog backpack compression, and for some other parts, it's nice, it has a rough exterior and seems to hold very well.
Tarptent also uses a similarly sized cord with its built in lineloc3 adjusters, somewhere in the 2-2.2mm range, and that also works well.
The stuff with the smoother exteriors I'd have some doubts about, both of the above are some kind of dacron type sheath over the core, and that seems to be fine with lineloc3, which is I assume also why tarptent uses that.
When you see it, you can tell that it will hold fine, I got zero slipping on my pack, nor on my tarptent.