how they could save over 50% of weight by maintaining the same power output
Except it, that new battery could have greater capacity, I can imagine one more way. I suppose that in standby mode the consumption of ELT is very low, lower then 1 mW and battery life is limiting by its self discharging process. In case of emergency, I suppose that the transmission of data is not continuous, that between data blocks could be time breaks, eg. 5s "telegrams" in 30s interval. If you have not energy enough, you can make intervals longer. My speculation.