The problem is fixed. I had 2 issues:
I was not using the version of SQL CE, SP2 that is supported by SQL 2012 (Cumulative update 7).
I did not have the SQL 2012 Replication components installed. I had SQL 2008 R2 replication components installed.
Once I fixed all this, replication started working. However, I lost the ability to use SQL Management Studio to manage my CE database. I now have to use the SQL Server Compact Toolbox.