Yes. A big problem with him is he was fighting super light for his size both at LHW and as a HW. Only in his final few fights was he anywhere near his natural weight. After he lost to Loughran he should have put on 25-30 pounds and this just didn't happen he trickled barely across the 175 limit like he was 5 ft 8 or something.
I'm pretty certain certain that James Braddock had the same issue as Fitzsimmons. Hand issues. Which makes his power tricky. Obviously Fitz had power. But just the minor tweak to your hand & all power goes away. Fitz had Gardner down & hurt his hand fighting him & was unable to do much after that to George Gardner...when he could of finished him fully healthy.
Braddock had hand issues literally his entire career. He could sting you but I guess the answer would depend on how you define puncher. He wasn't a knockout artist but you knew you'd been hit when he tagged you. Braddock gets a lot of crap here, with people thinking he was an outright jabroni. I have no illusions about where he belongs on the ATG list, but I think he was an excellent professional prize fighter who suffered from being a "tweener" size-wise plus like Jersey Joe his early record is deceiving because a lot of times he was ill-trained and fighting just to feed his family rather than to excel and move up the ladder; who's to say what might have happened with both him and Walcott in a parallel universe where they got quality training/guidance/management from the start and, in Braddock's case, some treatment on his hands?
He was a feared puncher @LHW until he fractured his hand. After that he showed sporadic flashes of power, such as his KO of Corn Griffin or KDs of Joe Louis & John Henry Lewis. This UP blurb from March 22, 1935, references "The famous right hand of James J. Braddock."
I wouldn't describe him as an out and out puncher, no, but at LHW I think he had decent power prior to his hand issues. Less so at HW.
In the Baer fight, the ring microphone captured the sound of his punches thumping on Baer's face. The right uppercut he hit Louis with sent ripples across his back. He could really hit with either hand.
I think he's kind of like Mayweather or Fenech,could crack both ways,either their opponent's skulls or their own fists
Slow afoot, unspectacular, well-schooled, courageous and a sharp counterpuncher with an educated jab and a good right hand. I'd make him a slight underdog against the lesser heavyweight champs of later years, e.g. Johansson, Weaver, Thomas, Berbick. Favored over Leon Spinks.
I think he would do better and against better folks than you listed, but you captured his strengths and weaknesses pretty well.