Yup, yup, yup, yup, yup, yup. Dumb dumb dumb.

I waited an hour or so then booked the skeleton itinerary I wanted (everything correct except trip connecting in BKK instead of SIN) and called a phone agent to ask for help changing it. I got a really good agent who handled the changes about as fast as possible.

"About as fast as possible" is incidentally about 42 minutes at this time of day — but of that time, only about 3 minutes was spent setting up the itin for the change, all the rest was opaque on-hold rate desk stuff.

There's no lesson -- except that if an itinerary which is obviously by-the-book correct and not weird at all will not ticket and gets pushback from an agent, maybe you need another agent.