Druapl 7 problems behind a proxy

I run Drupal behind an Apache Traffic Server caching proxy. In my setup, the proxy listens on port 80, and the real Apache HTTPD server listens on port 82 (which is firewall off). In my Traffic Server remap.config, I have a rule like

map http://www.boot.org  http://www.boot.org:82

Granted, in retrospect, this is not the best of setups, but it does however causes serious problems with Drupal 7, whereas it does not cause problems with Drupal 6. In D7, the favicon.ico and all JS and CSS URLs in the head are created to use absolute URLs. I don't set an explicit $base_url in my Drupal settings.php, more on that later, and this causes the URLs to get the wrong base! These URLs are all getting a form like

http://www.boot.org:82/misc/favicon.ico

Yikes! This obviously fails, since port 82 is not accesible from the outside. Browsing the forums, the "solution" seems to be to set the $base_url in the Drupal settings.php configuration file, e.g.

$base_url = 'http://www.boot.org';  // NO trailing slash!

This does indeed solve the problem, however, it now breaks when I want to use e.g. https://www.boot.org for admin access. Besides, why these URLs should be absolute, is a mystery to me, they certainly were not in D6.

The solution I'm ending up with is of course to change Apache Traffic Server to use what we call "pristine host headers", so that the Origin server (Apache HTTPD and Drupal) sees the original client Host: header. I could not get any help from the Drupal IRC, or forums, but if anyone has any insight on why D7 is doing this crazy stuff with absolute URLs, please post. In an ideal world, they really should change these to be relative, e.g. /misc/favicon.ico.

Hacking: