Thanks to bekabug for her suggestion on how to display a prev post link on the index page that contains the title of the entry in that direction. Unfortunately, I've been unable to extend it to the archive.php page, which as I understand it might be used to display a category, everything in a specified month, or a "tag" group -- so it would need to be a little versatile. I can get the next and previous page links to display using next_posts_link, but only with static text. Since I'm just displaying one post per page (with comments), I think it's appropriate to display the post title as the link text, but I don't want to use a permalink because they need to stay within the category.
Blog is at timeforclarity.com/blog.