>> Removing/replacing outliers is usually not considered as a good approach,

It is great that you are trying alternatives, but in general anywhere there is potential for noise or artifacts, NOT removing outliers is not considered a good approach. In behavioral experiments, it is routine to do this and you would be questioned if you didn't do any data cleanup after collecting some data from a bunch of subjects. Things may be different in imaging, but it seems that there is potential for noise and artifact just the same. Unless there is a reason to believe that funny things cannot happen in imaging, removing outliers either within or across subjects seems desirable.