the problem with when the swabs were taken is many places take two or three days to return a RT-PCR (especially in the USA). That would leave little to no time to fly 20+ hours.
where are you from? Do you know if your countries embassy issues the letter? Immigrantion told me if you bring an email from the embassy saying they don't issue letters that will suffice.
I flew JAL from LAX to NRT then NRT to BKK a few days ago. Great service, good prices, and plenty of room to spread out. (I laid down across 4 seats and slept on both legs).