To change back to patch 1.03 you simply have to move the 105.big and 106.big files out of your installation directory and use the original game.dat of 1.03.
Have you tried to uninstall the T3A launcher with the Windows programs utilities and did you try to run the installer as admin?
Thanks for the suggestions.
With respect to the Windows Installer problem that was preventing me from re-installing 1.06, I have been unable to solve the problem. After uninstalling BFME the first time, the T3A launcher did not appear in my programs list, so I couldn't uninstall it directly. I'm not sure if it was in the list prior to my uninstalling BFME, but maybe it is important to uninstall this first, for anyone looking to uninstall BFME in the future.
As for running the installer as administrator, this did not make any difference for me.
In the end I had to restore the windows partition from a backup disk image, and then T3A installed normally again. Maybe this is just an isolated error on my system (Windows 7, btw), but I'd recommend doing a backup before trying to uninstall BFME/T3A, just in case the process damages the Windows Installer.
In any event, I am psyched to be playing some BFME again. Thanks to the developers who have kept this game running!