Thanks for all the suggestions. If anybody can think of anything else, I'm open to suggestions!
My experience has been that when the grey tank is full, it simply backs up into the tub. Sure fired way to know the tank needs to be drained! Both the kitchen sink and the tub drain quickly. I thought at one point that might be part of the problem; so I thottled back on the release from the sink, but that didn't help either. My thought was that if there was a partial blockage, a slower release rate would stop it from gurgling in the tub. No such luck! I did run a snake from the kitchen sink, as near as I could tell, almost all the way to the grey tank. Ran into a T or elbow somewhere along the line that stopped me. We even cut into the grey water vent accessible through my closet and ran a high pressure sprayer into the grey tank to no avail. As for accessing the plumbing through the basement storage compartments, all mine are seamless molded plastic. I guess the only thing I haven't done is gone in through the tub p-trap connection - not looking forward to doing that!