0x80 is just a null byte with odd parity. What she apparently missed is that this is bog-standard Bell 202 AFSK (1200 baud) with 7 data bits and odd parity, and the data is ASCII. By throwing away the top nybble, she was throwing away the parity bit and the top 3 bits of the ASCII encoding of decimal digits. The fact that it was a parity bit should've been pretty obvious, since the top nybble flips between 0x3x and 0xbx in the pattern that you'd expect for a parity bit.
You can decode it with off the shelf software, throw away the top bit, and get back mostly ASCII:
$ ./minimodem --rx 1200 -f ~/helicopter.wav | tr '\200-\377\r' '\000-\177\n'
### CARRIER 1200 @ 1200.0 Hz ###
282 0002.3
#L N390374 W09432938YJ
#AL #NA 282 0002.3
#L N390374 W09432938YJ
#AL #NA 283 0002.3
#L N390372 W09432928YJ
#AL #NA 283 0002.3
#L N390370 W09432918YJ
#AL #NA 283 0002.3
#L N390370 W09432918YJ
#AL #NA 283 0002.3
[...]
I'm actually surprised that she missed / didn't mention this, considering her experience with signals analysis and demodulation. This is pretty much as basic as telemetry data modulation gets! Then again, as a reverse engineer myself, sometimes we get caught up doing deep analysis of something that later turns out to be totally trivial :)