Hi all.
I didn't want to just leave this hanging. Thanks to your helpful advice, I got the derailer to work properly. I'm very excited to have vanquished this beast, with your help.
I wish I could tell you what the original problem was, but that still eludes me. I took a day away from it, and just rode with the missing gear instead. When my head was clear, I took Frankenmike's advice and unhooked the cable from the derailer and moved the mechanism with my hand. It worked just fine through all the gears, eliminating the limit screws from the equation. So I just stepped back, unrolled the bar tape and just started all over again. I unhooked everything and pretended nothing had ever happened, started from scratch. The stars aligned and it worked perfectly the first time. It took, like, eight seconds.
I must've either been trying to get the cable too tight, or didn't have a housing seated properly or something. I dunno. But it works and this is a very good thing indeed.
Thanks especially to Frankenmike for that bit of advice, which I'll use from here on out, and thanks to everyone who offered constructive advice for a newbie when you didn't have to. It proves again that bike people are the best people.
Ride on.
Keith.