"Precisely when to turn the radio on"? We're talking aircraft up at F360 not A050 - they could easily be in range for 40 minutes. Have a look at Flightradar24 for how many high level aircraft would be in range - Marree-Oodnadatta would be a reasonable distance to expect comms within.
There's a good chance an ex-pat would be on board and even if not comprehension is generally good, particularly if you keep it simple and clear - conveying a latitude and longitude wouldn't pose a challenge.