I don't get why the district seat doesn't simply use approval voting. If I look at my local district, Nuremberg North, the relative majority with fptp is always with the CSU. However the more or less left leaning parties, SPD, Grüne, Linke always have a combined solid majority over the neolib spectrum FW, CSU, FDP.

With approval voting, my educated bet would be a higher approval for one of SPD or Grüne than for any in the neoliberal/conservative spectrum.

Same goes for many districts which produce paradoxical overhang seats, in both directions, like SPD in NRW, and CSU in Bavaria districts.