Thanks for the tips.

So, just got off the phone with United. Agent was studiously polite (and firm).

It turns out that even though:
1. I selected First (by clicking on the far right box)
2. I was able to choose a seat in the First Cabin

My fare that was booked was United Polaris (A).

So, basically UA told me that I was a) always in Polaris b) the computer showed me the wrong equipment because it's being changed over c) and because it was equipment that was being changed over, my fare was less than it otherwise should have been. And that I got a good deal as a result.

So, PSA - If you think you are booking in First, pay attention to your fare code. And be mindful that is probably not the plane you are going to get, anyway.