Such an entrenched technology that would take decades to replace across the planet.

I don't think that it'd really be necessary to alter the underlying protocol (well, you could make something a lot more elaborate with designated "receivers" and acks of transmissions, but I'm talking about something analogous to what humans already do, retransmitting in the event of collision). Humans do have to figure out whether someone's transmitting, but the reason you don't hear static on analog radios constantly is because they have a squelch feature, detect when there's a transmission present; the radio is already looking at the signal sufficiently to do the necessary work.

AM allows multiple to talk and also allows edge-case signals to be received. FM and digital is way more sensitive to weak signals being washed out where as even a washed out AM carrier can often be picked out of the noise enough to realize someone has a problem.