It's kind of a half-assed idea at this point. But I was thinking that, by forcing identically drawn boundaries, then it would force both parties to choose.
Now that I think about it more, it probably wouldn't work. Both parties would just grab squares that guaranteed their victory. It would end up ultra-gerrymandered.
I think the simplest definition of "fair" that most people would agree with (at least before being told who would benefit and the tribalism kicks in) would result in a distribution of representatives that roughly matches the distribution of the population at large.
That is, if the whole population of a state votes 60% for one party and 40% for the other, and there are a total of 10 representatives from that state, the fairest distribution would result in 6 representatives for one party and 4 for the other.
If by you saying it's "unfair" to Republicans by just having a final representative distribution that more closely matches the distribution of votes, then I'd argue that is indeed fairer and the current system is the one that's unfair.
https://www.rangevoting.org/GerryExamples.html
https://archive.siam.org/news/news.php?id=1237
https://news.cornell.edu/stories/2020/11/fairmandering-draws...
http://autoredistrict.org/