How to let capacitor fully charged before being discharged by a load?
I am assuming that cap is actually shown incorrectly in that picture and is actually tied to ground between on one side and attached between the 3108 and the 2nd booster.

You need a voltage sensing circuit across the capacitor that turns on the 2nd part when then cap is charged to some level with sufficient hysterics to keep it alive down to some other level. 

Perhaps a you can find a suitable SCR that turns on at the appropriate capacitor voltage and stays alive with whatever current your downstream circuitry is consuming until the voltage drops so low it can't supply that current any more.