the capacitor or a small recharable battery should work. i wouldn't worry abt the feedback. once the switch is off, there isn't any place for it to go. don't need the blocking diodes. how are u accounting for the light. in the finished product, if the bulb is and its' entire circuit is contained within the light socket, how do u keep the reflected light from interfearing with ur sensor? one idea would be to put the sensor in a wall mounted light switch. that would also give u a source of power to keep a processor powered.
once the voltage drops to 11v, is ur circuit going to continue to draw current or are u going to switch it out until the power is removed and restored?
if u used two stages, the power could be applied to one set of led's. the other set could be switched in with a photocell and a switching transistor. time delay, ur back to using a power source...a 9v rechargable bat and a ne555? put it on the second set of led's. or u could size a capacitor that would give u enough energy for the time required (size might restrict u here).
the more u add, the more the cost, the more chances for problems. KISS...