Thank you, RequestedDeletion, janet and Jean-Philippe.
One difference between the list provided by Jean-Philippe and my installation is the inclusion of pgsql. For each of the remi php collections, I have added pgsql, e.g. php54-php-pgsql.x86_64, 5.4.45-8.el6.remi, and php55 and php56.
Another difference is the version numbers. For example, in the php54 collection I have version 5.4.45-8.el6.remi while the same packages in Jean-Philippe's list are 5.4.45-9.el6.remi. Note the delta of version -8 and -9. Other packages have a similar relationship. My system has an earlier php55 package, 5.5.35-1.el6.remi, while Jean-Philippe's contains 5.5.36-1.el6.remi.
It appears, then, that I need to update my remi installations. I will disable the remi repo and run the update again. If that works as desired, I will attempt the update for remi.