LaMotta doesn't have much to trouble Archie with. His immense physical strength is negated by Moore's own.
First of all, Moore's lead right was made for southpaw Murphy. As for LaMotta, Jake stuck to middleweight and sometimes welterweight competition for a reason, despite having been an amateur champion at 175. Hatchetman rated Moore the hardest puncher he ever fought, harder than Walcott, Marshall, Bivins and Murray, all of whom Sheppard fought multiple times throughout his career. Lowry famously rated Archie's power even over Marciano's. Moore was two for two at getting Whitehurst out of there (the only man ever to stop Bert twice), the second time immediately before a 26 year old Liston failed twice to do this. Too much power, even for Jake at his best.