I think I mis-read your post about the sub's polarity switch.  It will have nothing to do with a common ground at the input shorting out a signal, but if you do have to reverse the inputs because of the common ground then - yes- you might have to flip the polarity switch to make up for switching the polarity of the input.  But in either case, the sub's polarity switch should be set to where it sounds the best.

Dan

Not sure my cables are long enough by I could try that. Thanks for the ideas.