I'm not sure why the simplest idea doesn't occur to me quickly, but I was out riding today, still experiencing soreness on the saddle. Okay, it's new, and my butt is not in bike shape, but still...
Then I realized I was riding a bit too forward on the saddle. D'oh! I slid back a little, and voila! Felt better immediately.
Not sure why I was riding on the nose so much; when I got fitted for the bike I was perched back where I should be.
Also had less neck pain today, and I'm convinced that's just a matter of getting in the miles.