I got the answer about why I was getting fewer options when changing the flight than when booking the new one, and thought I'd post it here in case others encounter the same thing.

The old flights were available to anyone, even non-elites, so they were booked in X class. But the flights I wanted were only available to elites (no X availability, but there was XN availability). When I tried to change, the change looks for tickets in the same fare class, which wasn't available. But when I tried to book a new flight, it let me book into XN because I'm elite.