[TYPO3] setting up page with 404 status whose content gets taken from a page with ?id=18

[Surer Dink]

Setting up 404 pages properly appears to be a very frequently
discussed topic on this list, yet I have managed to not find anything
that would even hint to me how to accomplish what I am searching for -
I have a "site map" page that contains many useful links.  I have
managed to set up .htaccess with RealURl to properly serve pages and
used

$TYPO3_CONF_VARS['FE']['pageNotFound_handling_statheader'] = 'HTTP/1.0
404 Not Found';

to return 404 for pages that are not found.  however the 404 page just says:

Error. Reason: "..." could not be found, closest page matching is ...

I would like to instead show the contents of my sitemap page (which,
incidentally, is usually rendered through a templavoila template).
Can someone please point me to how I can accomplish this?  I do not
want to use a redirect - I want to serve a page, with 404 status, but
I want its contents to be the result of rendering the page with pid
that I specify.

Thank you for your help.