@jonmlewis, take a look at the Photon sleep modes, specifically the DEEP SLEEP mode:
The Photon has an onboard RTC (optionally battery backed) which can keep track of time but it does drift. When you connect to the Particle cloud, it resyncs itself but since you are running off the grid, this will not be possible. You may want to consider a more accurate, low drift I2C RTC to provide an accurate time source. The rest is all in how you calculate the number of seconds to DEEP SLEEP so you wake at the desired times.