Thanks again for the replies. I gingerly went out today, my first ride in a week. I leveled out the saddle like you said, but it just didn't feel right to me. There was too much pressure on my groin, which was what led to the scary numbness and pain I had last year (which I subsequently solved by lowering the nose of the saddle). So I compromised and tilted it halfway between level and the nosedive in the photo above. Honestly, that feels much better to me. I think I'm going to stick with it this way, for now.
I raised the bars slightly, as well, but after last week I'm not so concerned about neck pain anymore.
Oh, there is about 2" clearance for my bike as per your test, so I guess the bike is the right size, after all.