We accomplished this through Unity Connection.
1. We created a CTI for our pilot number in CUCM and sent it to Voicemail (Unity Connection).
2. In UC we created a System Call Handler for that extension.
3. We set the standard greeting to a recording we found online that says something along the lines of "Please enter your conference bridge number". We found ours professionally recorded online from a free audio file website, but you can record your own if you'd like.
4. On the greeting page, we selected "Allow Transfers to Numbers Not Associated with Users or Call Handlers"
5. In "Default System Transfer" we added the extension blocks for our CMRs to allow a transfer from the Call Handler back to CUCM to access the CMR.