My forum default sitemap has this
<lastmod>' . gmdate(DateTime::W3C, $result['lastmod']) . '</lastmod>
You have this
<lastmod><TVAR LASTMOD></lastmod>
If i change yours with my site default sitemap will work to get the last modify date and not the date sitemap is created?
Also i'll post new issue,
on my site i have 19,528 posts and your sitemap has 4,776,as you can see there are missing too much almost everything.
On the script configuration "Maximum depth level:" i have set "0".