The majority of these projects have pursued LEED-NC. I'm not aware of any that have done CS - but there is movement to extend LEED-H to high-rise residential projects, and I think that Pilot program may be open, so it's worth looking into it.

There are several advantages that LEED-H offers over NC in terms of how credit requirements fit the project type, and the integrated deesign benefits of personal contact with a local Rater who provides project review, site inspections, and energy benchmarking.