He was 28 years old when his rematch with Billy Smith was filmed, and had another win over Bert Lytell before 1946 was out. Two years after taking Archie Moore to school, I think we can make a case this is still a prime Burley, if no longer peak. Smith was a pretty good LHW, and his second round knockout of Harold Johnson in 1954 has been widely viewed on youtube. Charley didn't have his dander up as he reportedly did for the loquacious Mongoose, but it's still pretty telling that he handled the significantly larger Smith with such ease. Oakland Billy would draw with Moore over 12 six months after Burley-Smith II. We're hardly seeing Wills against Uzcudun when we view Charley in action against Smith. Burley, with his conservatism, skills and lack of punishment absorbed, was able to enjoy a long prime.
Its hard to pin point, given the fact that Burley wasn't always at his best given the fact that he was working a factory job, fought on short notice, and basically had every advantage stacked against him, so he was bound to turn in some uneven performances which distort how we perceive his form at the time.
I would seriously nominate vs Shorty Hougue. This fight reads like one of the great demolition jobs of a very capable and bigger fighter.
For a peak performance, this is not an irrational conclusion. It came during the midst of a career best 20 fight willing streak for Burley [the stretch between Bivins and Charles I], barely a month after Pearl Harbor. Two months later, he demolished Jay D. Turner. Although Turner was certainly no world beater, and had already been blasted out in one by Mauriello, he was still a big heavyweight with a winning record, quality experience, and a couple of decent scalps over the ten round limit in veterans King Levinski and Babe Hunt [who had height and reach on Turner in their exchange of wins]. Johnny Shkor might not be the worst comparison to Turner. Figure Burley had to be up for that one. He had a rough patch of four defeats through the latter half of 1942, as the war effort kicked in and world titles got frozen. Diminishing morale as he realized he wouldn't get an opportunity at a suspended championship, combined with the distractions of munitions work in support of the war effort surely further undermined the consistency of his focus during wartime. That doesn't necessarily indicate a decline in his potential. If any outcome suggested any slippage in that respect, it may have been Lytell II in February 1947.