Site map (TOC for full category hierarchy) on a separate place?

I'm just getting to know the category module, so please forgive me if I've missed something.

I'd like to create a site map on a separate place for a site organized via this module.
I've followed the superb tutorial Creating a basic hybrid structure and set up this structure on a test site. However, I'm getting stumped on how to create a site map on a separate place that reflects this same structure. I know that if I enable the TOC on the articles container and set its depth to negative I can get immediately a site map on the Articles container page (it's so cool! Thank you for this great module!); but I don't want the site map to be there, I'd like to be able to have a separate site map with that TOC.

So far I've tried to: change the hierarchy to multiple, and set the separate Site Map page as a parent (fails spectacularly); allow Distant Parents (works somewhat, but I can never get the Articles container page to show up, and so the hierarchy is not reflected accurately); create a weird site structure with hidden containers (doesn't work). Am I missing something obvious, can this be done at all? Any help would be appreciated.