Personally, in the age of computers, I don’t see why it would be so hard to do a completely nonpartisan redistricting by using a computer algorithm to draw boundaries around N geographic regions (where N is the number of Congressional districts) such that each region has roughly (within a specified margin of error) the same population, bearing in mind not to split residents of the same street address into different regions, with the minimum combined perimeter size around all regions.
Considing existing political & geographic boundaries (street, precinct, city, county lines) and compliance with the Voting Rights Act and the "one man, one vote" standard.