You can get the gamma value from the ratios, but you are still making assumptions. I don't know how many accurate temperature and pressure readings there are at 70,000ft.
I'd suggest you are looking at a gamma value of between 1.3-1.4, as soon as you get that high you can use pV=nRT a little better as the air is so "thin" there are less molecular collisions and so these are negated, but are still present.
You might want to email NASA, I'm sure they have some data on this. You can get up to 80,000 ft on here, temp there is 199K
U.S Standard Atmosphere
Don't forget when you do your calculations to use only SI units, ie Pa, K etc