I think intentional OTT-ness requires at least some understanding or compassion to be done in a way that's effective? And for something that's meant to be deliberately offensive for artistic purposes, she seems awfully surprised that people were...offended. Which makes me think it was really just a very poor joke and makes me less inclined to give her any benefit of actually having been attempting to subvert any stereotypes

Yeah to all of that. Undoubtedly you've already seen this, but just to get it out there, a couple of quotes from the Boston Area Rape Crisis Center blog:

See [Palmer's] continued misuse of the word “rape” in interviews, and the simulated rape of a Katy Perry lookalike in her stage show. [See the blog post for the YouTube link.] Suffice to say I’m not optimistic about her handling of this, simply based on her track record. ...

Palmer has posted a non-apology in which she at least half-acknowledges that her choice of words regarding disabled feminists was poor. But despite numerous comments on both of her blog posts asking her to address her trivialization and flippant use of child pornography, she has chosen not to address it, instead editing that part out of the original post. (In her followup, she actually calls herself “brave”.)

In her non-apology, she says this is art and art is controversial, and we just don’t understand, and - oh, look, I have bingo! Again, I disagree. This isn’t art, Ms. Palmer, it’s cynical, dismissive marketing. If it was art, you’d have the guts to actually examine the realities of the trauma you’re putting on like that conjoined-twins dress.

That might be worth watching.

In a comment, Shira adds:

Unfortunately for Palmer, intent is irrelevant. When one does something that is widely perceived as harmful, one can consider why people feel it’s harmful and fix it, or one can dismiss everyone that feels hurt and say “That wasn’t my intent, so you’re not allowed to be upset about it.” Palmer has once again chosen the latter.

I've casually enjoyed the Dresden Dolls (which is not to say I haven't found at least a couple of their songs failsome about stuff like intersex and trans issues), but I'm not talking about any boycott (to be sure, a boycott is an action targeted against specific institutions of power, anyway) when I say this whole thing is repugnant enough that it's unfortunately going to shadow my experience with the rest of Palmer's work. I would say Webley's other work, too, but I'd never heard of him before this.