My first response might have echoes to the Doing DH v Theorizing DH discussion in that it aims toward the pedagogical side that is (sometimes) seen as being under the DH umbrella.
If you count public blogging about a class as part of DH (itself a performance), then that's one way to go at it. We had an experience here a few years ago in which a student in theatre was blogging about her difficulty in how to direct a particular scene of a play. A few days later, the playwright commented on the post. It was a really powerful moment for the student.
And, I've worked with one professor who is taking public domain video and audio from Internet Archives to have students create a soundtrack to a video.
For other facets of DH, I can definitely see the difficulty in talking about performance art . . . harder to mine data from a performance than from a text!
That said, here's the kind of idea that I would throw out, as one example of how performance art and DH could mix:
Given that so much of new media is (re)mixing content and media together, there might be rich ground for combining live performance with how people currently do mashups? That is, a mashup of both live and digital?
I think that there are core DH ideas -- new media, remixing content in new ways -- that combine with more traditional performance art lurking in there somewhere.
Hope that helps...I'll be interested to see where this conversation goes!