For whatever reason, the problem I was trying to solve seems to have gone away. I can type in firefox's search box without midco stealing searches. Something changed resolv.conf behind my back. search midcoip.net is there again. I hadn't rebooted or changed firefox's preferences. I'm guessing it was when I turned the connection off and on. To be sure my joy was not tempory, I rebooted. midco still not stealing searches.
I wish I knew what the problem had been and what fixed it.