It will take a bit of wiring, but replace the single pole switch for start up with a double pole, run the black wire from the convenience outlet to one side of the switch, then run a wire from the other side of the same pole back to the black wire of the convenience outlet.
For the other pole, keep the wires the same. Use a meter to make sure you get the wires on the correct side of the switch poles - you don't want to turn on one thing while turning off the other.
Sorry for your loss.