I've just watched a documentary about the No Wave, just now. They talked mostly about:
Christoph Dreher (of Die Haut), Jim Jarmusch, Nick Cave (& The Bad Seeds) and Lydia Lunch, while showing bits of lots of other bands that I forgot, [I just remember James White & The Blacks].

If you want to check it, it's called No Wave - Underground '80: Berlin - New York (2009) by Christoph Dreher.

Would Nick Cave really be considered No Wave?

not really. your manifesto is interesting, but i disagree with the exclusion of popular music forms. remodernism seems to me like it should be about embracing everything so long as it strives for authenticity.

I'm glad you found the Manifesto interesting. The Manifesto is an experiment, not something that we're totally bound to 100% of the time. For example, I agree very much with Remodernism, but reject it's rejection of post-modernism. That's why I included the last clause of the Manifesto, because in the end, a Manifesto becomes a totalitarian tool that dictates art, which it shouldn't do.

On a side note, I think I could see certain early Nick Cave recordings like "Saint Huck" fitting the No Wave aesthetic

I think the Birthday Party are more classifiable as no wave than any of his solo stuff, but even so I wouldn't really call it no wave. He has worked with (and probably f'ucked) Lydia Lunch though, so there's a definite connection.

Maybe Richard Kern filmed it

You know, Jim Jarmusch is connected to punk and no wave cinema, and he founded the "Sons of Lee Marvin" 'secret society'. Other members include Thurston Moore and Nick Cave.

Bit of a stretch though. Nick Cave and Lydia Lunch together would certainly be classifiable as Cinema of Transgression though, right?

Well.. today we would just call it "celebrity sex tape" but if Kern filmed those two going at it in the 80s he certainly would have claimed it as Transgressional Cinema.

crabs and the clap

Wasn't Jarmusch himself in a no wave band (probably briefly)? I'm sure I read that somewhere but was never able to find anything by the band.