Well in the end it just took one phone call, very good timing and rather good luck.

I called to sort out our seat assignments on the return and while I was on the phone I inquired about the nonstop option for the outbound. The agent informed me of the ~$100 change fee but the fare would decrease (we were on a moderately high economy fare), so I went ahead with it. But the reason for the fare decrease was actually that she'd priced the change with the wrong return date -- the correct dates would actually entail a large increase, as one would expect. When she discovered this, she put me on hold to reverse everything out. In the end it took probably over an hour, but because of the lack of availability on our original flights she ended up switching us over to the nonstop, retaining our upgrades, and only charged us one change fee (fare increases were waived).

Worth noting it probably helped my case that I stayed cheerful throughout the long wait, she thanked me repeatedly for my patience. Could be wrong, but I suspect if I'd gotten snippy and impatient, she wouldn't have tried so hard to make it all right for me.

Kudos to CO.