Can you make sure that the MOH you want to play is uploaded on all the CM/MOH servers by going to below location of all the CM/MOH servers individually
Cisco Unified CM Administration >> Media Resources >> MOH Audio File Management
Also, please reset the CTI ports from CUCM. You will need to go to Cisco Unified CM Administration >> Device >> Phone and then do a search like below:
Find Phone where Device Name begins with <Device Name Prefix> that you have configured for the Call Control Group in UCCX. This way it will list all the CTI Ports for that particular Call Control Group, select them all and do a reset.
Regards
Deepak