Update
I took my CX 4 out for a ride this afternoon. Here's the weird part. Although I could feel this soreness in my behind when I sat down on a chair and (especially) when I got up again, I did not feel it at all during the ride. I felt a little stiffness on the outside of my behind, as the saddle is somewhat firm. But no additional soreness. Then I realized that this soreness only started some time after my previous ride. Could it be that it wasn't the saddle at all, but that I could have pulled something back there? It reminds me more of a pulled muscle than anything else. Does that make sense to any of you?
I also tried padded bike shorts for the first time. When I put them on, they had an odd "bunched-up" feeling as I stood. But, said I, if they help the ride, I can accept that. And they do seem to help. I'll do a ride each day and see how things go.