As to djp's suggestion about a "listener".... I like it!
Contrary to what tuj says, "listening", with modern technology, would consume far less power than regular "pings".
So pinging for a few weeks, then listening for a few months, is a good idea. It would need a new module inside the FDR and CVR (or rather inside the beacon), which doesn't exist yet, so whether there will be enough of an impetus to update the beacons, for what is a rare occurrence, is an open question.
The boxes would have to only listen say every 15 mins for a few seconds as the search vessel can carry a high powered transmitter and sensitive receiver which is operating continuously with a ping/listen cycle. if the CVR/FDR hears the ping during its listening period it immediately responds with its reply ping which is repeated for say a few minutes.
In this way, power consumption during idle periods would be minute; probably in the order of microamps, just powering a timer.
James