In case someone finds this through search, here's the problem. The WordPress documentation says two different things with respect to category archive pages:
1. Here it says you can use query_posts to restrict a category page to a specific category:
2. Here it says use of query_posts will cause WordPress to ignore the page value, which condemns you to just a first page of listings:
The documentation clearly needs to update at least the Category Template page to note that use of query_posts will cause WordPress to ignore the page value, thus preventing pagination links from working within a category page.
I'm also amazed there don't appear to be any documentation pages about pagination, how it works, when it works. That would have saved me a few hours wasted time.
In my case, I'm creating section home pages around specific categories. Since I can't use the category archive pages, I'll have to hack it by customizing versions of single.php, creating a blank (wasted) page for each section, assigning the new template to the page, and then in the new template manually including a link to the full category archive. Basically a ton of wasted time and needless complexity because WordPress doesn't read the page value when you use query_post.