Thanks TheUnassuming. I wasn't adding the carbodiimide last, so that's definitely something I'll try. Unfortunately the only solvents that dissolve both compounds together are DMF and DMSO.
I looked into the acid chloride route, it seems reasonable in theory, but my colleagues who have done acid chloride chemistry warn that it can be quite difficult. Plus, my lab is more formulations based, I'm not sure we have all the right equipment anyway to do an effective and safe reaction with something like thionyl chloride.
The mixed anhydride chemistry looks attractive. I wasn't aware of the triofluoroacetic anhydride reaction, that is a great suggestion, and I think I might give that a shot while I try a few other reactions with the DCC.