As of now GBH has a number of limitations that makes it unusable for any moderate complexity query.
We need to enable GB key columns save/restore that was previously done by tntnatbry saving them in create_columnstore_groupby_handler() and restoring in columnstore_groupby_handler::init().
The second flaw comes from MDB's optimizer that can optimize out 'needless' GB keys from the query. We need to try Monty's suggestion(ask me about the details).