CTI has absolutely nothing to do with softphone, and is expected NOT to work, the MRA documentation clearly states it.
CTI is for DESKPHONE control, which is also stated in the MRA documents as NOT supported.
Softphone mode does not rely on CTI. It uses SIP to register.
CUC, once again, absolutely nothing to do with CTI, you need to white list the servers to which your users might also connect.
With that in mind, I would suggest you to review once again your config, make sure the traversal zone is up and running, DNS as required is configured, and all the necessary certificates and root certs are all installed in the relevant servers.
HTH
java
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