Hey Ed
I had some popping problems with the Heartthrob Tremolo. I ended up putting pulldown resistors on the switch lugs at both circuit input and output to stop it. Worked a treat! Although your situation is much different.
You could try rewiring the switch to ground the OD output like this
but I've no idea what that would do to your input signal
You could go all out and wire up Pulldown resistors everywhere or add (more) blocking caps in series with all circuit outputs.
Bear in mind though...I have next to no idea what I'm talking about!!
Good luck