Maybe have each drone regularly broadcast their GPS's most recent NMEA sentence (latitude, longitude, timestamp, altitude, etc.) signed with their public key?

That's what came up with after thinking about it for a bit. There's probably a better solution out there.

Pretty sure we have solved this problem, since we use HTTPS

Who cares? Are you suggesting setting up an agency that monitors 'airspace' (I wouldn't call area 20 meters above ground an airspace)?

I don't want my drone to be seen at the moment of crime anyway.

Don't like drone in front of you? Accidentally throw a piece of string on it.