Hi again,
So the 1000uf cap just has to keep the LED on for a second or two, is that the only reason for the 1000uf cap?
If so, you can use a diode. Disconnect the top of the 1 ohm resistor from the relay, insert a diode cathode to the 1 ohm resistor anode to the original connection (relay). Disconnect the top of the 1600 ohm resistor from the relay, connect it instead to the cathode of the diode.
Now when the relay turns off, the capacitor only supplies current to the LED not the node at the far right. When the relay turns on, the capacitor charges again.
If the 1000uf cap also has to filter the output from the relay so the far right node gets a cleaner supply, then simply add another 1000uf cap at the far right node from the node to ground.
Is that what you needed?