Also, if you're going to go straight into fantasy land to solve gerrymandering, you can just do party-list proportional representation by state, or STV for smaller states, and then there's no districting at all. There's nothing in the constitution requiring congressional districts at all.
If you cannot expect congress to act in the peoples' interest the only viable solution is through federal court action. In the mean time, since I am in fantasy land (as you call it), I will prefer practical solutions no matter how improbable in the real world over constitutional amendment which is even more imaginary.
Also there is no reason to expect increased seats in congress will have any effect upon gerrymandering and may even make it substantially worse. It certainly won't make law making more efficient.
And while you could try to gerrymander an 11,000 seat House of Representatives, it would be a lot harder.
* All boundaries of a congressional district must be either a state's boundaries or fixed to a single latitude and/or longitude and meet at an approximate 90deg.
* Exceptions to the prior mentioned rule are acceptable only in the cases of remainder space, which is space remaining for a congressional district only after the prior rule is otherwise fully executed.
* Remainder space districts must not be adjacent.
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An alternative approach:
* Congressional districts must be limited to county borders in the case of low population density districts that may comprise multiple counties or subdivided entirely within a single county for high density districts.
* Subdivision of a county must occur strictly upon either points of latitude or longitude, but not both and cannot exceed the borders of any single county.
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I believe the shape and size of congressional districts should be flexible to account for variances of population density. I happen to live in a state with a huge population and perhaps the most wild fluctuations in population density. For horrid examples of gerrymandering view our current congressional districts: https://en.wikipedia.org/wiki/United_States_congressional_de...