Just google soft jaw pliers, theres nothing special about the Iwata ones ! Im sure your local hardware has some
I did look into regular soft Jaw pliers. Comparing pictures, the Iwata ones are actually "special", in that they have a bite cutout which is both radiused to generally match airbrush body diameter, and toothed. They're designed to grip almost all around the knurling, instead of on relatively small patches of it. Which was part of the problem with all of the pliers I had: they're toothed, but the bite cutout of "normal" pliers is always too ovoid relative to the brush body diameter, so grip (and thus sheer force) is concentrated in small areas, which is what leads to both slippage and stripping the knurling.
Soft jaw pliers of similar geometry to the normal metal pliers I had been using would fail for the same reasons (insufficient contact area resulting in force being over-concentrated for the materials), it's just the jaw rather than the knurling that would be the softer material, and thus would take the damage. Unfortunately, this sort of thing is all I could find. There does not appear to be a "general use" brand of soft jaws with a bite profile sufficiently similar to the Iwata ones.
All the similar-sized soft jaw pliers I found in my internet searches either have too-ovoid jaws, or jaws with a diamond-shaped rather than circular radius. All were untoothed. Most tooth jawed nylon pliers are larger sized, with even more relatively ovoid bite profiles.
The only reason I even suspect the Iwata pliers ever might work is because of the bite shape should at least give a much better contact area. I just worry it might not be enough if the spring screw is on there tight enough, and it's a lot to spend on a tool that seems like it'd be a coin toss it not only wouldn't work, but would also destroy itself in the attempt if it doesn't.
If you know of any that actually are similar, and are affordable enough to be sacrificial, I'd love get a pair. Unfortunately I wasn't able to find any myself.