For what it's worth, Phil and production could have taken one of these flight combos:
(CM) Copa Airlines 650
(BOG) Bogota, CO to (PTY) Panama City, PA
Actual Departure: Actual Arrival:
4:58 AM - Fri Nov-20-2015 6:31 AM - Fri Nov-20-2015
(UA) United Airlines 1022
(PTY) Panama City, PA to (EWR) Newark, NJ, US
Actual Departure: Actual Arrival:
9:34 AM - Fri Nov-20-2015 2:32 PM - Fri Nov-20-2015
(UA) United Airlines 956
(EWR) Newark, NJ, US to (GVA) Geneva, CH
Actual Departure: Actual Arrival:
5:43 PM - Fri Nov-20-2015 7:07 AM - Sat Nov-21-2015
Or they could have taken these flights and arrived around the same time:
(CM) Copa Airlines 650
(BOG) Bogota, CO to (PTY) Panama City, PA
Actual Departure: Actual Arrival:
4:58 AM - Fri Nov-20-2015 6:31 AM - Fri Nov-20-2015
(CM) Copa Airlines 304
(PTY) Panama City, PA to (IAD) Washington, DC, US
Actual Departure: Actual Arrival:
9:22 AM - Fri Nov-20-2015 2:06 PM - Fri Nov-20-2015
(UA) United Airlines 974
(IAD) Washington, DC, US to (GVA) Geneva, CH
Actual Departure: Actual Arrival:
5:44 PM - Fri Nov-20-2015 7:22 AM - Sat Nov-21-2015
This is not necessarily the fastest way, but one that works and arrives way ahead of the teams. Also, it fits with the timing of the tweet Phil sent yesterday afternoon.