M9 - here's how I would think of doing it - not had to try in practice. Radio messages are not that long, you just need everyone else in the queue to give you next turn.
Regardless of current radio traffic, squeeze PTT and say "Mayday, Mayday, Mayday .... [callsign]". Release PTT
Repeat as needed in rapid succession.
The current transmitting aircraft will not hear you whilst they are transmitting, and everyone else gets "2 at once screech". If current transmitting aircraft ends his message before you do, the word "Mayday" will be heard and everyone goes quiet for your next call. If not, by repeating the process everyone else on frequency knows that someone is desparate to break in and shortly the current transmitting aircraft will finish their message and you will break in.
Once in, you can deliver your message