How to have a timely departure from FCO:
1) Book a 6am flight on British Airways
2) Have a pre-arranged taxi driver pick you up at 3:55 am.  While you are casually standing outside your apartment building, trying to not look like a lunatic or a modestly-dressed streetwalker with luggage to the bemused bakery workers loading up goods for delivery.
3) Make sure the taxi driver makes like a Formula One driver through the empty Rome streets.
4) You will walk into the terminal door at 4:18 am.
5) Go to the designated check-in counter, where there is no line, and check in. Walk past the Air France (and probably code shared with Delta) check in line with about a hundred people in it. Try not to be smug. (Of course they are probably flying direct, so they have their own reason to be smug)
6) Go through a rather indifferent security.
Settle at your gate and think about what you’re going to do for the next hour of free time in an empty airport where nothing is open.
I have no travel alarm clock, and my phone is a stupid Verizon phone, so it’s not Europe-compatible, so my solution to the “I’ve got to get up at 3:30 am dilemma” was to have Michael call me at 8:30 his time. Perfect. And a better wake up call than a hotel computer.
By the way, the Gatwick employees are just so polite. I hear about the decline of service in England, but I guess they’re keeping Gatwick up to speed. The equivalent of their TSA people were just so terribly helpful.  The person assisting us in loading our things through the x-ray machine was practically motherly. And he was a 40-year old guy. “There you go! That’s right! Thanks so much! Lovely!”