Thank you both for your very helpful comments!
@jcolombo, I was hopeful when I looked at the links you gave me about the Brightcove RSS feeds, but I'm afraid they won't work after all. The information they contain only refers to video players and not the videos themselves, so that won't allow me to get at the actual video files. It was a nice thought, though!
@MSGreg, I had thought that what you were referring to was impossible in Brightcove, but it turns out that they do reveal the URLs for the actual video files! Here's their information on it:
http://support.brightcove.com/en/docs/b ... #mediaURLsIn looking at my various videos, it appears that they are all in a folder named with my publisher ID, so I think I could make a relative URL from that. The only trick is that Brightcove says these URLs change "from time to time":
The most important thing to remember is that the URLs for images, video files, and renditions are not fixed. Brightcove reconfigures the storage of media assets from time to time to meet requirements of some change in our internal systems, to improve performance, or for other reasons.
However, for $300 a month, I think I can afford to check myself every day to make sure the links are still working, and update the XML file if necessary. On second thought, maybe I could write a program to do that for me!
Anyway, just wanted to post my findings for you and for anyone who may stumble across this thread looking for answers. Thanks again!