I was referring to Erwin Schulz in this case. He has a brief Wikipedia profile:
https://en.wikipedia.org/wiki/Erwin_Schulz
I was referring in particular to his profile in Michael Wildt's book about the RSHA's leadership corps. 'An Uncompromising Generation'. It's a really, really good book. He's one of the three Einsatzkommando leaders the book discusses in detail as part of collective biography of the RSHA leadership. I really cannot recommend it enough.
To clarify, Schulz was not a good guy. As Einsatzkommando leader during the campaign in the Soviet Union, he still ordered the murder of thousands of Jews. And he continued to faithfully serve the Third Reich as an SS leader after being recalled. He was still a Nazi. But he seems to have drawn the line when the Einsatzgruppen started murdering women and children.
Due to manpower shortages, many of the people under his command were cadets of the Security Police school, of which he was basically the inspector-instructor, so they were essentially his students on top of being his subordinates. When he asked for a transfer, he persuaded command to cut their deployment short, using the argument that their present mission was taking too much of a toll on them psychologically (which was definitely a thing in the Einsatzgruppen and Police Battalions, it's one of the reasons the SS built the gas chambers, though the Holocaust by bullets continued alongside the Operation Reinhard death camps).
Long story cut short, Schulz was recalled back to Berlin, promoted and given a different job. His colleagues and many of his subordinates thought he was a 'wuss', but he wasn't harmed.
Regarding Six, I agree that he probably thought this was beneath him, though being sent to head a murder squad in the East was a career opportunity for many and not a punishment in the SS - Ohlendorf's career benefited from it and Erich Ehrlinger was promoted to RSHA department head pretty much solely on the basis of his successful record as the incredibly murderous leader of an Einsatzkommando. It was a chance to 'prove your toughness and earn glory'. I'd say Six would've probably been responsible for more murders if Moscow had actually been taken (or if the unspeakable sea mammal had succeeded thanks to ASB intervention).
See, he used to run an 'academically' orientated department in the RSHA, which was supposed to 'scientifically and historically analyse Jewry, freemasons and other ideological enemies' and stuff. But that department didn't work out because its purpose was rather...obscure and so it didn't last long. Plus I get the sense that he wasn't good at office politics, which put him at a disadvantage when dealing with ambitious colleagues and his rather overbearing boss.
So he probably perceived running his new job as a comedown. He didn't even get to run a full Einsatzgruppe unlike his colleagues Nebe and Ohlendorf (Vorkommando Moskau was attached to Einsatzgruppe B, which was run by Nebe, a man who'd been Six' peer in the RSHA). The RSHA under Heydrich and later Kaltenbrunner expected its members, especially its senior figures, to have a 'soldierly attitude' and be ready to move from murdering people from behind the desk to murdering them at the 'frontlines'. I'd say Six had no ethical problem with the killings, but liked doing it from behind a desk more and felt his department wasn't being appreciated enough.
He was involved in the SS's operations to murder the Polish intelligentsia following the German invasion. Moreover, he openly supported the Final Solution in his new job at the German Foreign Office after being recalled from the East in a speech to the 'Jewish specialists' and 'Aryanisation advisors' from the German embassies, saying the 'physical annihilation of the eastern Jews would deprive Jewry of its biological reserves' and this was great since the Jews were the sworn enemies of Germany and controlled the allied powers. Worth noting that he continued to rise in rank in the SS after switching jobs. He was an SS-Brigadeführer when the war ended. Lutz Hachmeister wrote a biography about him, though I don't know whether it's been translated into English, and Wildt also talks about him in his RSHA study.
Fun fact, the section that was responsible for studying the old Catholic Church's persecution of witches was located in his old RSHA department (though Six was no occultist or neo-pagan type).