Actually, thats not that hard to do . . . if you're me or John. It would be fairly difficult for a someone who hasn't spent a lot of time around electronics.
Basically, you'ld replace the bypass switch with a small relay. It would have a fair sized cap across the coil wires - say 4500uf. When you switched it off, it would take several seconds for the cap to discharge and for the relay to disengage.
Better yet: the relay would be powered by an op-amp. The input of the op-amp would be taken from the output signal. As soon as the delay degraded to inaudible, the op-amp would switch the relay off. Perfect sync.