We trust people with responsibility all the time. Seems an odd objection. 
Any method of grouping is going to result in dissimilar people being in the same group. An algorithm that starts with large population centers and divides and/or expands along existing boundaries (local government, road networks, geography) until they are balanced would be my preference.
A variation on the old “I cut, you choose” solution. Each party draws up it’s own map. A committee decides which is less gerrymandered using objective purely mathematical criteria. Said committee to be comprised of two Dems, two Reps, and a chair chosen by majority vote of the members.
If you can’t find two people in each party who can be trusted, when mandated to do so, to serve the public interest rather than that of party, we’re in bigger trouble than I think we are.
Don’t forget that one reason for gerrymandering is giving minorities a proportional vote so any redistricting plan would need to meet this judicial requirement.
I haven’t forgotten that. What some people call “majority-minority” districts, I refer to as “electoral ghettos”.