WOW!!! So I'm definitely aiming too high if that's the case.
The thing is, like I said before, once you release the balloon there's no way back (you know this), so if things don't work like you expected, the whole project is gone...
With this I mean that I would try to get the code and everything as simple as I can. I may pick a SF a little above what I would expect to be valid and try to use the best antenna I can.
Now that you've done this before, let me ask you something if you don't mind.
What antenna did you use both for the payload and the chaser?
What GPS module did you use? I'm using for these tests the NEO-6M Ublox GPS but this one doesn't go beyond 18Km in height, so Im awaiting for a NEO-8M to arrive, which does go beyond 18Km.
Any help on this topic would be appreciated, Im a teacher collaborating with 9 kids in this school project and I can't fail with this 
Thanks in advance