For RW, Adam's Double Softs are the recommended ones to use. The cheap ones won't pick up dirt nearly as well, likely smearing it, and they can induce micro scratching as a result. Not recommended for paint, as you said, but they work just fine for door jams, engine bays, and wheels in my experience.
The non-glass towels you got are 600 and 400gsm, while the Double Softs are 920gsm. Can't vouch for how the ones you got would work, but Adam's are softer. Even the SST are 800gsm, for comparison.