Watching that video made a design sketch flash into my brain. Instead of using Time to regulate the pulse charging ... use Voltage! Use an op-amp comparator to monitor the voltage on the Capacitor as it charges up, and flip to the dump mode when the cap reaches the setpoint voltage!
This would be ideal for compensating for varying solar illumination because with variable input to the PV it will take more or less time to get the cap to its optimum voltage for discharging into the battery. If you use regular time intervals, the cap will sometimes have more charge (voltage), sometimes less, depending on the input light at the PV panel.
So using the op-amp comparator will allow you to set the voltage at which the cap dumps into the battery and also automagically compensates for varying input power as from a solar panel, charging the cap to the same voltage but taking longer or shorter time intervals to do it. Also you can just put in different cap banks and the system will automagically compensate, because it takes longer to charge a bigger cap to the same voltage, etc.