What is C+? Are you using KVS? Very few of us use it for finding DL award space because it just pulls from DL.dumb (buggy and with phantom KL space) or AF.us (space not available to DL) or, if you know where to look, the JL website for AF space only.
I'd use ExpertFlyer to find the AF/KL space. The AF space won't be phantom and will be available to DL. Unfortunately, the KL space might still be phantom. Also search DL TATL routes and look for it to price as low (100K is the lowest, since there's no such thing as a one-way priced award on DL). You should then be able to assemble everything via multi-city.