Even if you make our own profiles and everything is perfect, you still have to deal with inconsistency in the process. 
Grays are tough to do well and really separate those that can from those that struggle. Be ready to make you own profiles as well as relinearizing and reprofiling if it has to be tight.
For those that make their own profiles, if you want stable greyscale output (without color anywhere), read your icc patches normally then generate the icc with VERY high K generation, a zero start for K, and very low total ink. Something like K start=0, Max K=100, total ink=200, max GCR. Then the only trick is to send only grey files. Don't expect this ICC to convert any color, just handle greyscales.