is there a way to setup a custom home page at blog.tld/category ? or even at blog.tld/category/xyz ?
Perhaps I misunderstood what you want when you say “custom home page at a non-home address”.
Your first example tld/category
by default will be a 404, since that is not a URL that WP has, unless you create a Page with that slug. That is what my theme provides a page template called “Taxonomy Root” for. If used on a page with a slug that is a taxonomy, it will list the links to all the term archives of the taxonomy, along with whatever content you put into the page.
Your second example tld/category/xyz
is already handled by WP, and is a list of posts with that term. You can’t add content to the page since it is generated dynamically, but you can put any content you want (including HTML) in the term description, and make sure your theme displays the description (my theme does) on the first page only.
As movies are a good example, if each post is a movie, and there are custom taxonomies for director and actor and filmtheme, using default category for genre, you can see how one person set it up using my theme by going to the Actors page. This is a Page with the Taxonomy Root page template used. He could have put more content, but didn’t. I know he put some content in some of the terms (maybe film themes?), but there is so much there, I’m not finding it right off…