Districts should be deprecated altogether. Instead we should elect representatives via proportional representation.
When we we had approximately 30,000 citizens per representative there was a chance at your representative actually knowing you, but at this point we are more likely to have our views represented by a third party.
Norway is below your 30,000 citizen per representative number, and frankly even then, while there certainly is a chance, not many people do know their representative even there.
In Norway, some regional connection is arranged by grouping seats into multi-seatconstituencies by region. Then more proportional results are obtained by taking any votes "leftover" for a party after assigning whole seats and assigning seats from a non-geographic pool with some caveats.
It satisfies those who want a regional link of sorts, and doesn't skew the proportionality too much.
For the US, I think that electing representatives by proportional representation within states would work similarly and would work pretty well with our existing constitutional framework.
When we we had approximately 30,000 citizens per representative there was a chance at your representative actually knowing you, but at this point we are more likely to have our views represented by a third party.