Why do you need individual data for gerrymandering? Don't you only need area level?
Once you've table voter preferences to actual street addresses you are no longer in the realm of "broad area cumulative averages and medians".
Also see: Nashville, Tennessee
Like your dormroom example, ATX is very progressive.
I actually made jigsaw puzzles to advocate against gerrymandering. They were difficult to solve! michaeldnahas.com/doc/jigsaw_puzzle/index.html
It's much worse, now.
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The fact that there are non-contiguous US Congressional districts (e.g. TN's 2nd/3rd have inholdings within each other) makes the entire process even sillier.