So, solved, I believe, by creating a file '/etc/resolv.conf.tail' and putting the line '192.168.0.1' in it. Now everything works as it should.
/etc/resolv.conf does look like this, when I started up:
So that's that.
# Generated by dhcpcd from wlan0
# /etc/resolv.conf.head can replace this line
Blargh. Things broke again--now it the probelm occurs intermittently: sometimes it succeeds in resolving, most of the time not. In addition, the network connection when it does succeed is extremely slow, with huge lag on things using the network, like irssi.