I have taken several COVID tests (and had COVID), as well as had my family tested several times (and my daughter got COVID as well). All the test results I received had a draw date/time and a report date/time. When I checked with the airline they told me they look for report time since that is when you should be notified and get the results.
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).