I think that in the case of the US one start point is to look at the history of changes, that would offer a huge clue to the extent of gerrymandering in a particular area.
The point made by @NorthernPiper seems to be the most important, how the boundaries affect representation by lobby as you go upwards through the representative heirarchy.
We had significant boundary changes in the UK with the creation of certain port counties in 1972, in particular Humberside. This took areas from previous historic counties and was almost universally despised even before the Law came into effect. The idea had been to create one area of common interest around a large port estuary which might appear logical given that there are many ports of varying sizes and loading stages both north and south on the estuary.
Those changes were driven by administration practicality rather than by gerrymandering so the motive was very different.
In practice, the estuary is so large that the logistics of it really didn’t work out well, it was divided into the northern half and southern half by the river, and at that time the only link was by a pretty modest ferry.
The thing that really did for it though was the pretty roughshod manner that overrode the public sentiment in a sort of ‘we the policy makers know what is good for you’. It was percieved as arrogant imposition and rightly so because it turned out not to be a great idea anyway, and the issue of common interests for the maritime activities could easily handled in other ways.
Humberside was largely unpicked in 1996, and actually increased representation at Westminster Parliament because the return to the original boundaries meant that more Members of Parliament then were able to band together in House debates.
All I am saying is that it can work both ways but public sentiment is also important - areas often develop along corridors of access so its not surprising that you might get unusually shaped districts if you go by common logical interests.
I think that there really should be some sort of US electoral commission, but your division of powers makes it difficult to do this on a fully national scale, perhaps there should be a system of appeals process where concerns can be taken up to an equivalent of a Supreme Boundaries Commision similar to how the courts system operates.