You can extend the battery life very easily by reducing the ping rate most of the battery power is expended in putting acoustic energy into the water.
Halving the ping rate would do something close to doubling the battery life (assuming the design of the device is competent, which I assume it is).
If the number of search vessels is large enough, the reduced frequency wouldn't reduce the chances of the beacon being found. (Each vessel has to travel more slowly to have the same chance of hearing a pinger which uses a lower ping rate, so each vessel searches a smaller area - so you need (roughly) twice the number of vessels if the ping rate is halved).
I'd be in favour of not activating the pinger for the first 96 hours to allow detection vessels to start to be deployed in the area, followed by a couple of weeks of operation at the current ping rate, then a further month at a reduced rate (by this time, you know you're not going to find the recorders easily, and have had time to assemble a decent search fleet).