Ideally a beacon should transmit every so often last known position & depth (5,10,30,60 minutes?), but be listening as well. When it detects a trigger signal, it will go into full transmit for 1,3,6 hrs? It would then revert to the previous mode to save battery until triggered again. It would be good if it transmitted the received trigger signal strength too. The trick is that the beacon receiver will be affected similarly as the surface receivers are. Signals can be blocked by terrain as well as thermoclines (temperature layers in the water that can reflect/refract signals), however the surface trigger transmitters can have a lot more power. Of course ideally you don't want to be transmitting whilst trying to listen, so the beacon would need to know to transmit at a set minute of the hour (:00?)
In this scenario you could drop 100's (1000's?) of buoys with the transmitter & receiver over the suspected area, thus covering a much larger area more quickly. Some of the buoys could be designed to sink to a specified depth & the return to the surface (or part of the buoy) to transmit a found beacon.
At the moment it seems a bit old fashioned the way searching is done. Even today 1000 receivers could be made, dropped on the area, slowly sink down to the seabed & then if one of them detects a pinger, release a transmitter back to the surface & transmit its location & depth of detection. Hopefully several will pick-up the signal & a map can be made to narrow the location further.
Can we do better with today's technology than we are at the moment?