The Big Red One isn't nearly as exaggerated, which isn't to say Fuller has lobotomized his style. I love the image of Lee Marvin disguised as an Arab, chomping on his cigar through a layer of wardrobe. Marvin tells his men that "killing is not murder" and in the very next scene we hear a German leader tell his soldiers the same thing. That's Fuller all over. See also the French leader who insists his men should fire on the arriving Americans, including the image of the leader dead, but still firing at Marvin and his men. It's blackly absurdly funny, but just inside believability.
What you don't mention here is that the French leader is then killed, and all the soldiers immediately decide to lay down their arms and join the Americans because they didn't want to shoot at them in the first place. My problem with the Big Red One (well, one of them) is that Fuller seems to be completely torn between a desire to denounce/satirize war (the asylum scene, the attitude towards death and killing) and celebrate it : the ending of course, but really the whole film felt schizophrenic to me in that respect, and the concentration camp scene is the worst of it. You see it as a way to humanize Lee Marvin's character : I'd go further and say it seeks to make him into a hero.
Now ambiguity isn't a bad thing, but it didn't feel like ambiguity to me as much as Fuller theoretically wanting to make a film satirizing war and ending up doing a piece of propaganda. It's not so much "war is insane", as "war is really tough but ultimately worth it and soldiers are clearly heroes to be celebrated". To be clear : I don't think it's an invalid point of view to have, but the film is too schizophrenic about it to even come close to making it work.
What do you think about the constant sunny weather throughout the film ? It makes it look like they're on vacation almost, contributes to it feeling like an asepticized version of war. Basically I founds the film to be completey thematically dissonant, and the concentration camp scene was the confirmation of that : you're saying it humanizes Lee Marvin's character, but he is always portrayed positively throughout ! Yeah he's rough, but he's the leader and he cares about his core group of guys : I don't think there's any attempt to make us feel ambiguous towards him : he's the typical sergeant character in those war films.
It feels as if we saw different films, which... I'd rather have seen your version.