If I remember correctly, didn't someone finally come up with an algorithm which evenly divides populations such that average distance from the average location of the district residents is minimized? A law which mandated use of that or a similar algorithm for district boundaries would actually help. Just moving the problem into committee obfuscates the problem.
Independent committees have historically been pretty effective anti-partisan solutions. One prominent example being the CBO, which both parties like to stand up for while in the opposition, and disparage while in power.
When districts are not competitive (and especially when unlimited secret campaign donations are allowed), the primary campaigns end up driving candidates toward radical positions, because the primary is the only competitive stage of the process.
What we’ve seen with the GOP is a party that has moved sharply away from mainstream opinion, subjects all of its officeholders to strict purity tests, and is largely controlled by religious hard-liners and big donors (oil, defense, pharma, banks, telecoms, etc.), and has become increasingly anti-intellectual and overtly bigoted in the past few decades.
I had a colleague (mathematician) who suggested presenting district-ers with a dramatically distorted map of the region to be districted in which neighbourhoods were unrecognisable, and all that could be seen was population density. One could gerrymander such a map all one pleased, but with (presumably) no better than random chance of thereby accruing a benefit, and random risk of suffering a detriment.
There are undoubtedly other factors to consider than proximity and party affiliation. The key takeaway is that districting is an opinionated act, algorithm or not. If we're going to "solve" gerrymandering, we need to figure out what "successful" districts look like first.