Respectfully, I will disagree and hope our discussion is helpful to the OP to understand both our positions. OP can go test your cheek weld hypothesis, and next time I go out, I will test it myself. I have never experienced it before, which is why I asked for more information.
1) OP has a 5/8 riser on his cheek so it isn't as low as you might think. I have solved most cheek weld issues with less than two pieces of camping matt and athletic tape. I have also gotten rid of my "cheek weld" and gone to a gentle "jaw index" because a "cheek weld" was too much pressure and induced shooting inconsistencies. In the end, any cheek or jaw weld is an index to make sure we assume the same position.
2) OP said he was accurately hitting steel. Suddenly, he started missing but then after adjusting his zero, he started repeatedly hitting steel for another two hours. It doesn't sound like he is having issues with changing positions. He used the term "about 4 inches low". I can't say for sure, but at 400 yards, if I were spotting and had good trace, I could probably make a guestimate within inches. We often say, "one target low" or "one target high". He said:
I shot at the same target and was hitting about 4 inches low. I then shot at a 200 yard steel target and was hitting around 3 inches low as well. I re-zero'd my rifle and dialed to 3.75 again and began hitting steel at 411 yards again and had no issues for the rest of the day (about 2 hours).
3) OP had a second shooter verify that the zero was low.
4) The only "mechanical" issue I am aware of from changing head position that would move a group is parallax induced error if he does not center his eye in the scope. And, at the distances he is shooting, he would have to go from one extreme scope shadow looking like a moon sliver to the exact opposite direction with a moon sliver.
We all know that a consistent cheek weld is important for good shooting, but I have never seen that changing cheek weld move a zero that dramatically. Typically an inconsistent cheek weld just makes the groups bigger over all.
Edit to add, you have to make the assumption that he made one dramatic change to his head position and wasn't bouncing between them during the day. To the OP, I would be curious if he did make any other changes between the apparent zero shift.