It is actually possible to render vbAdvanced modules in normal vB pages, you just have tweak things a little to give the CMPS module code neough of its environment to do it's business.
Here's some sample code I use for doing almost exactly what you are wanting to do, where I place the "News" mod in certain profile pages:
Code:
define(CMPS_NEWS_MODID,4);
$save_modules = $modules;
$modules = array();
$modules[0] = CMPS_NEWS_MODID;
$mods =& $vbulletin->adv_modules[CMPS_NEWS_MODID];
$mod_options =& $cmps_options['adv_portal_' . $mods['identifier']];
require_once(DIR . '/includes/class_bbcode.php');
$bbcode_parser =& new vB_BbCodeParser($vbulletin, fetch_tag_list());
require(DIR . "/modules/news.php");
$modules = $save_modules;
$welcome_bits = $home[CMPS_NEWS_MODID]['content'];
So hang the above code on some suitable hook in profile.php (probably profile_complete), Then just use $welcome_bits wherever you need it in your profile template. I actually run this code on vb 3.7, using a class extension rather than a hook, as the whole way the profile page gets built is different in 3.7.
Also in my app, the define() line above is actually in a config file. You'll have to change that to define the module ID you want, and also change the require() path, to the module php you want.
To find the ID of the module you want to use, go to the CMPS 'Edit Modules' page, and check the URL's as you hover over the links.
The above code may or may not work for the Recent Threads module, but I think it will.
-- hugh