"I've disabled the Windows Wireless Zero service, as I'd heard that can cause problems, but I still get the disconnects"
You could well be better off disconnecting all the third party WiFi Managers you are using and use the Windows Zero Conf throughout. Generally that's recommended on this forum.
It may be worthwhile changing the Channel on your Airport (try 1 then 6 then 10).
When you restart your computer does it reboot the Router?