I'm interested in using Aegir to deploy Drupal websites. I'm wondering if there is a way to customize the user experience of setting up a new site, while still maintaining the Aegir mechanism. Probably something more like the standard Drupal setup screen.
Yup, create a theme with all things you want, some custom modules to do more heavy lifting and there you have it and install both on your Aegir server. (working on similar idea i have for Aegir, including fcgi support, so i can jail sites to a user, sell them in a store and let the users fix their own sites.)
And / or you could use something like http://drupal.org/project/hosting_services to write something yourself. (and loads more)