Hi Michael,
If I understand you correctly you want a specific project to executed directly from the root domain of your site but still physically reside in project_web directory.
If you're running Server 2008 IIS check out URL Rewriting and add an Inbound Rule that can capture the requests to the root domain and properly redirect it to your application. You can also capture parameters.
here's a quick example.
I have an inbound rule that uses regular expressions and watches for this;
^rdp_session/([_0-9a-z-]+).rdp
So anything coming in to the website with a path of /rdp_sesssion/-any text or number-.rdp will then route to the following url in the background;
/myproject_web/us/handle_rdp.awp?s={R:1}
The rdp file is passed to the awp file as the 's' parameter.
Make sure you set the action type to Rewrite.
If you're running Server 2003, you'll want to check out one of the add-ins that give you the mod-rewrite / url-rewrite functionality.
Cheers!
ken