I've made progress, but I'm still not having luck.
Both servers are now running 12.1.2 (I upgraded the old server, then installed the new software on the new server, after uninstalling the old software on the new server, if that makes sense).
On the Management Server Configuration Wizard, I've walked through all the steps. It gets to the point where it says "The database is being created and initialized. This will take a few minutes." After a minute or so, I get the error:
Unable to connect to the server specified.
At the previous step, when I choose the replication server and enter in the connection information for the old server, everything was fine (other than the "do you trust this certificate" message). Any ideas?