Have to run but here are a few instances where Charles places his head unnecessarily in range, as a fairly stationary target. Marciano doesn't really take advantage of the opportunities Charles gives him in some of these clips, but I think they show the tendency I was talking about nonetheless. https://streamable.com/gm0di https://streamable.com/rciio https://streamable.com/igjs9 https://streamable.com/3mee4
In the second two, it looks like Charles was getting worn down. In the first two, Charles' head is in optimal position. When he gets in close he keeps his head in a position where Marciano has to punch at an inopportune angle thus making Marciano's hand nearly useless.
Charles tries a left hook. Rocky blocks. Charles jumps out of range and tries a jab. Rocky evades the jab and bombs over the second jab. I used that to show while Charles had trouble jabbing. But it doesn't fit your description of Charles' leading with power punches and getting caught. Charles lands a left to the body and clinches to avoid a counter attack. Charles lands a 1-2 and clinches to avoid a counter attack. Charles pushes Rocky off and looks to create space, but Marciano bulls in off a feint and appears to clip him with a left hook. Interesting, Charles gets caught doing something you criticized him for not trying, creating space and using his feet. This is the only clip so far that fits what you were saying. Charles lands a right cross but can't smother Rocky on the follow up as he had been doing previously, and Rocky manages to squeeze off an uppercut before the clinch. I wouldn't say head movement was the culprit here, Rocky was just a freak and took a nasty shot to land one back. Ha, I actually used this clip to show Charles' head movement. Charles gets clipped with a weird right uppercut, he fires back and uses his head movement to get out of trouble and avoid most if not all of Rocky's follow up blitz.
The third is the only one that fits his description but Rocky absorbs a monster right hand and follows up with the uppercut. I'm not sure what you could do to avoid that, other than not throw the right hand, which would only lead to Rocky bulling in on you. Helpless situation. The 4th, Charles gets hurt and shows some great movement to get out trouble.
In the first gif, it seems like he's trying to establish exactly that. He achieves his rhythm for about a second, until Rocky regains control of the pace. The second gif, Charles is no longer trying to establish his pace. He's trying desperately to keep up with Rockys pace. He find just enough room to land a 1-2, and weaves all the way around. I see him trying desperately to create room and space in a very dangerous environment. The third gif is Charles displaying his strength to try and gain Rockys respect. He stands his ground, lands a hard right, pushes Rocky away, and stays in place. He most likely did it as a defense mechanism, to earn space from Rocky. I don't think he simply forgot to use head movement. He's hurt in that 4th gif. He looks hurt and out of ideas. Rocky is on a very aggressive attack, and doesn't let him clinch. That first uppercut by Rocky was a beauty by the way. Look at that form.
The commentary is post-production, explaining how the fight will unfold in restrospect. The footage shows Charles trying various things, before settling on a strategy of hitting and holding. Which works until the mid rounds. Charles certainly was doing something right, other than standing still as Maricano swung wildly as you implied originally, the first round is a shut out for him.