I have the same setup that you do and I have tried to simulate the same problems that you have. Except, I have the Add on Manager, not the Universal Installer, and everything works fine for me.
I have a feeling that when you removed the Universal Installer something got undone with your sim.
I have only one suggestion left, if that was my computer, I would give some thought to going back to basics and uninstalling all of the FSDT products using windows control panel and re-installing them to see if that fixes things for you. Uninstall all the currently installed products AND ( important ) reply YES to the question "Do you want to remove the Addon Manager ?"
The Universal Installer replaces the Addon Manager on a new install so it should work for you and get your airports back. Just make sure you have a copy of the activation codes if you decide to uninstall and re-install.
If your not 100% sure about it, then ask for a second opinion. I had to do that awhile back to fix a few problems and it worked well for me.