What has not been mentioned by the previous posters suggesting HF is that nowadays huge chunks of HF spectrum can be recorded using SDR and played back at leisure, with particular attention to transmissions sticking out as unusual. Likewise VHF, if anyone is recording it in that way.
This is interesting because intelligence networks like GCHQ do something along these lines and as the aircraft was equipped with something like Rockwell Collins HF 400W transceivers which can work any frequency between 2 and 30Mhz then it is possible those on the cockpit had capability of communicating on preassigned frequencies with a range of 1000s of miles.