OK, for some closure - and in case any future newbies have this happen as well - my subsequent work has demonstrated that I think that first chip was defective right out of the package. I had 5 other sensors and I soldered the headers onto all 5 today, and with a setup just like van_der_decken's here, all 5 worked.
So I'm chalking the first one up to either something I did that we can't narrow down, or just a defective chip.
Thanks to all who pitched in to help me!