What format are your clips and your project settings?
Am I simply denying that the 720 multicam clip and timeline will throw away pixels no matter what, and that I am better uprezzing my one 720 angle in a 1080p multicam clip and timeline and exporting at 720?
My experience with FCPX is that down converting from 1080 to 720 works well – certainly better than dropping 720 clips into a 1080 time line.
Do you have an orange bar above your clips?
Try exporting a short test section and open in Quick Time to see whether you still feel it's soft.