I'm not proposing this as if it's the magical solution to all interviewing problems. Bad interviewers and bad interviewees will still exist. I'm trying to address a particular problem... if you, as an interviewee, do not like coding on whiteboards, and you're concerned that your skills will be reflected poorly, well...
try to solve the problem then. If an interviewer won't let you solve this well-known and acknowledged problem, well, you certainly learned something about the interviewer, too.
But if you didn't even try to solve the problem, don't come whining to me (on the internet).
That said, I would also recommend just dodging all these other technical problems. Maybe spend 30 seconds trying to get the projector going, but if it goes beyond that, just say "Let's just look at the screen here on my laptop". Unless you've being interviewed by more than 3 people, it can be managed. Come equipped with a full battery. Etc. But this is all manageable stuff... I manage to get this right for trips to the airport, surely one can manage for a job interview.