Another Old Clematis Problem

My godfather has a very old and rampant clematis (I don't know what group, but it flowers only once a year, in the spring). It was trained up through a cedar tree in his back garden, but has become so heavy over the years that the stems have sagged out of the tree and block access to the rest of the garden. In addition to pruning the flowering stems at the top of the cedar, he would like to train the old stems back up into the cedar branches. However, these are now so thick (5-15 cm diameter) that any forced movement causes cracking within the stems.

Any advice is welcome, but particularly regarding tidying the trunk-like stems. Can we prune one or two of them off without killing the whole plant? Should we try moving the stems only a few centimetres a year? Should we just start again?

Thanks