So this is how it went:
N and I arrived at Austin-Bergstrom International airport at 6:30 a.m. for a 9:30 a.m. flight to Dallas, intended to connect to a flight to Philly, which would take us to Rome.
Instead (thanks to the Blizzard that Crippled the Midwest), we flew to Chicago (genius) to connect to a flight to London and then to Rome. After people laughed at us when we said we were flying out of Chicago at 5 p.m. on Tuesday (blizzard warning started at 3 p.m. and lasted until 3 p.m. on Wednesday), we called the airline and asked to be sent someplace southern, quickly.
That worked, and we flew to Raleigh-Durham for a flight to London, and then to Rome.
All told, it took 4 flights in a little over 24 hours, and a little running through some large airports, but we made it just 6 hours later than originally scheduled.
Sadly, our checked luggage was not as lucky.