The 5D MKIII is already compressed, it shoots in H265 format which is great for shooting but not good for editing.
H264 uses a GOP format (group of pictures) where frames are compressed across a series of other frames.
This gives a small file size but is not ideal for editing as the decoding has to be done "on the fly".
For editing in FCP you should use a frame based codec, ProRes.
ProRes is not as highly compressed as H264, hence the increase in file size. You do not lose any quality when you do this.
ProRes is also capable of supporting higher quality pictures than the 5D can produce so that is why there is no gain in using HQ or 4444 as you have already exceeded its spec.
You need to go to th 5D MkIII page on Canons site and go to the downloads section. Download and install the EOS Movie E1 plug in for FCP - that will allow you to use the log and transfer tool.
Hope that makes sense.
best wishes
Neil
http://www.patience.tv