So... I bit the bullet and paid for a month's subscription at FlightStats. (If you guys have anything to search for let me know!)
Here're my best guesses for the Panama to Sao Paulo flights:
Matt/Redmond, Vanck/Ashton (as described by travel agent)
CM725 from Panama City to Sao Paulo, 1542-0035 (scheduled 1543-0045)
Shamir/Sara, Seth/Olive, Brooke/Scott (as described by travel agent)
CM703 from Panama City to Sao Paulo, 1824-0309 (scheduled 1832-0330)
Liz/Michael
They're seen boarding an Avianca flight in daylight, so it probably wasn't Copa to Lima and a night Avianca flight to Bogota. They arrived before London/Logan, so the best fit is:
AV8375 from Panama City to Bogota, 1738-1917 (scheduled 1750-1920)
LA3505 from Bogota to Sao Paulo, 2136-0534 (scheduled 2130-0550)
Didn't put them on AV8383 from Panama City to Bogota (1045-1214) because they would probably have made it on AV249 from Bogota to Sao Paulo (1500-2310).
London/Logan
The Insider video had them at Gate 32 in Bogota, so they took AV85 from Bogota to Sao Paulo, 2203-0558 (scheduled 2204-0615)
The most logical flight from Panama City to Bogota (on the same airline) would have been AV8375 from Panama City to Bogota, 1738-1917 (scheduled 1750-1920), the same flight as Mike/Liz.
Becca/Floyd, Joey/Tara (shown on a Copa flight, and arriving after London/Logan)
CM749 from Panama City to Sao Paulo, 2130-0628 (scheduled 2114-0620)
Jessie/Francesca (London/Logan say they transferred via Mexico City in their Insider video)
AM625 from Panama City to Mexico City, 1606-2007 (scheduled 1615-1950)
AM14 from Mexico City to Sao Paulo, 0048-1227 (scheduled 2325-1055)
Wow, an extra 1h30 delay on top of a late scheduled arrival!