All three timers generate interrupts which can wake the processor from sleep (depending on the sleep level). In particular Timer 2 can wake it from a deeper sleep (SLEEP_MODE_PWR_SAVE).http://gammon.com.au/interruptsand:http://www.gammon.com.au/forum/?id=11497
Would another option be to configure the pin as a port change interrupt before going to sleep? After waking I could reconfigure the pin to act as the event capture. I would lose some timing accuracy at the beginning but I am not sure that will matter much.
The event capture of Timer/Counter 1 seems to be a good way to do this because the time stamps will be really accurate.