Basically I don't want to have to choreograph this that carefully

You shouldn't need to choreograph it that much, after 06:00 there are fast trains every fifteen minutes that go direct from London Victoria to Gatwick. You just need to make sure you wake up...

http://www.gatwickexpress.com/

If you decide to stay near the airport there are dozens of hotels around the immediate area. Make sure when you book that they have a courtesy bus from the airport to the hotel, most of the big ones should have.