Here's a fresh look at all the possible flight routes that teams could take going from Fortaleza to La Paz.
The constraints I have used to make this collection are
1) Teams can catch their flight out as early as 2 am on April 26th
2) Teams must arrive at La Paz airport by 2 pm in the afternoon of April 27th
Turns out there were quite a few ways to do this. But, each team will have to make their flight out of Fortaleza using one of these six flights to Sao Paulo or Rio:
FOR GIG JJ 3255 2:40 AM 5:50 AM
FOR GIG G3 1995 2:50 AM 6:20 AM
FOR GIG G3 1826 6:00 AM 9:25 AM
FOR GRU G3 1403 6:05 AM 9:50 AM
FOR GRU JJ 3325 8:00 AM 11:30 AM
FOR GRU G3 1773 11:50 AM 3:30 PM
And, at the arrival end, each team will have to arrive, April 27th, on one of these five flights from Lima, Miami, Cuzco, or Santa Cruz
LIM LPB TA 39 9:30 PM 12:20 AM
MIA LPB AA 922 11:10 PM 5:30 AM
CUZ LPB 5L 451 8:00 AM 10:55 AM
VVI LPB 5L 450 6:45 AM 7:45 AM
VVI LPB 5L 126 1:00 PM 2:00 PM
For teams that use the VVI as their connection they will have to get there through Buenos Aires, Sao Paulo, or Lima.
Here are th e full itineraries for each arrival mode:
Arriving from Lima
FOR GRU G3 1403 6:05 AM 9:50 AM
or FOR GRU JJ 3325 8:00 AM 11:30 AM
GRU EZE RG 8632 12:00 PM 3:00 PM
or GRU EZE LA 4551 1:55 PM 5:05 PM
EZE LIM TA 24 6:00 PM 8:45 PM iffy
LIM LPB TA 39 9:30 PM 12:20 AM ar April 27th
Arriving from Miami
FOR GRU G3 1403 6:05 AM 9:50 AM
GRU MIA AA 2944 10:50 AM 6:05 PM
MIA LPB AA 922 11:10 PM 5:30 AM ar Apr 27th
Arriving from Cuzco
FOR GRU G3 1403 6:05 AM 9:50 AM
or FOR GRU JJ 3325 8:00 AM 11:30 AM
GRU EZE RG 8632 12:00 PM 3:00 PM
or GRU EZE LA 4551 1:55 PM 5:05 PM
EZE LIM TA 24 6:00 PM 8:45 PM
LIM CUZ LP 17 5:15 AM 6:30 AM 27-Apr
or LIM CUZ LP 25 5:20 AM 6:35 AM 27-Apr
or LIM CUZ LP 21 5:40 AM 6:55 AM 27-Apr
or LIM CUZ 2I 1115 5:50 AM 7:00 AM 27-Apr
or LIM CUZ Q6 237 6:00 AM 7:00 AM 27-Apr
CUZ LPB 5L 451 8:00 AM 10:55 AM 27-Apr
Arriving from Santa Cruz via Buenos Aires thru Sao Paulo
FOR GRU G3 1403 6:05 AM 9:50 AM
GRU EZE AR 1263 7:35 AM 10:30 AM
or GRU EZE RG 8630 8:30 AM 11:30 AM
or GRU EZE JJ 8010 10:20 AM 1:10 PM
or GRU EZE AR 1241 11:00 AM 1:55 PM
or GRU EZE G3 7453 10:50 AM 1:40 PM
or GRU EZE RG 8632 12:00 PM 3:00 PM
EZE VVI 5L 211 4:00 PM 5:45 PM
VVI LPB 5L 450 6:45 AM 7:45 AM 27-Apr
Arriving from Santa Cruz via Buenos Aires thru Rio
FOR GIG JJ 3255 2:40 AM 5:50 AM
or FOR GIG G3 1995 2:50 AM 6:20 AM
or FOR GIG G3 1826 6:00 AM 9:25 AM
GIG EZE AR 1251 9:50 AM 1:05 PM
or GIG EZE JJ 8016 10:30 AM 1:50 PM
or GIG EZE RG 8616 10:50 AM 2:20 PM
EZE VVI 5L 211 4:00 PM 5:45 PM
VVI LPB 5L 450 6:45 AM 7:45 AM 27-Apr
Arriving from Santa Cruz via Sao Paulo
FOR GRU G3 1403 6:05 AM 9:50 AM
or FOR GRU JJ 3325 8:00 AM 11:30 AM
GRU VVI 5L 301 4:00 PM 5:45 PM
VVI LPB 5L 450 6:45 AM 7:45 AM 27-Apr
Arriving from Santa Cruz via Lima thru Sao Paulo
FOR GRU G3 1403 6:05 AM 9:50 AM
or FOR GRU JJ 3325 8:00 AM 11:30 AM
or FOR GRU G3 1773 11:50 AM 3:30 PM
GRU LIM TA 141 6:05 PM 9:00 PM
LIM VVI TA 35 9:55 PM 1:30 AM ar April 27th
VVI LPB 5L 450 6:45 AM 7:45 AM 27-Apr
Arriving from Santa Cruz via Lima thru Sao Paulo
FOR GRU G3 1403 6:05 AM 9:50 AM
or FOR GRU JJ 3325 8:00 AM 11:30 AM
GRU EZE RG 8632 12:00 PM 3:00 PM
or GRU EZE LA 4551 1:55 PM 5:05 PM
EZE LIM TA 24 6:00 PM 8:45 PM
LIM VVI TA 35 9:55 PM 1:30 AM ar April 27th
VVI LPB 5L 450 6:45 AM 7:45 AM 27-Apr
So, in summary, the best possibility will be the route leaving as late as 8:00 am from FOR to GRU to EZE to LIM to LPB arriving at 12:20 am on the 27th.

That route does contain an iffy connection time of 45 min in Lima. Maybe that is too risky

, so the next best route leaves at 6:05 am from FOR to GRU to MIA to LPB arriving at 5:30 am on the 27th.

All the routes using Santa Cruz arrive as early as 7:45 am on the 27th (if the 7:45 am flight is full they have to use the next one arriving in La Paz at 2:00 pm). The Cuzco way will put teams into La Paz at 10:55 am on the 27th.