I can't believe I found these, but I found the biography on William Shatner (which has my favorite part in part 1 at the 11:20 mark in which you find out where Shatner's distinctive method of speaking came from) and
Beyond the Final Frontier (embed disabled) one that's supposedly about the fans and hosted by Leonard Nimoy, but it mainly about a prop auction. There are some good things spliced in like some talk with fans and some people like Patrick Stewart or Nichelle Nichols talking about stuff, so it may be worth a watch anyway.
Click to view
Sadly, I couldn't find the captains of the Enterprise special anywhere. Maybe there should be an e-mail campaign for Bio to show it again. :(