I haven't sen that done before but I suppose it could work. And the ability of CCEA to use custom ensembles would be a natural way for you to run the final analysis: just treat your several solutions as individual members of an ensemble and let the algorithm do its thing.
Getting to that point would be labor intensive for you, however, I agree.
An old-fashioned way of giving more weight to under-represented attributes is just to replicate their columns in the database. For example, let's say you have a 10 level attribute and a 2 level attribute. If you want to give the two attributes equal weight you could just make 4 more copies of the columns containing the utilities for the 2-level attribute. Now you have 10 columns for your 10 level variable and 10 columns for your two-level variable. I've always thought of this approach as being a bit clunky, but perhaps it's a fit for your need.