Line passing with sleep

I have line passing working just fine.

I am trying to minimize my current usage.

The remote is set to Cyclic Sleep Remote with Pin Wake-up and is working great. The signal when sent lasts for 1.25 seconds.

The base is set to Cyclic Sleep Remote (SM = 4). I want it to sleep for a second and wake for a second (or less) to cut the current draw in half and also ensure that I never miss a 1.25 second signal.

I can get it to sleep for one second then wake but the shortest wake time I can get is ~5 seconds.

This is for a remote Canadian area with limited battery (6v 4.5 Ah). There is also limited sun available in the winter time for charging.