Is that really that impractical?

With a quick calculation 50 ms time offset would mean about 20 meter difference. You can get that accuracy with NTP over residential internet and a better TCXO could hold that for a day. You could sync clocks and download the almanac at each airport. The almanac could be digitally signed and NTP has an option for authentication, too. That's about 10 USD of hardware (plus what you need for image capture and processing).

I'm pretty sure with dedicated hardware and better solutions you could get much better accuracy.