Answering myself here -- hope that's permitted.
All my poking around hasn't turned up any news ticker software that will work with OS 7.5.5. But I have found a few text-only or very graphics-light news sites that the computer's able to handle. Namely:
http://news.bbc.co.uk/low/
http://thin.npr.org
http://ipsnews.net/text/
Probably not enough for me to actually keep the computer on my desk, but it's a small start.