The M26 Pershing will indeed fit in an LST [not sure about a LCT] and the 70th Armor's DD Shermans hit Utah beach from an LST launch about half that of the Omaha landing, one reason the casualties at Utah were not as horrible as those at Omaha. And, of course, during the Inchon landings, the 70th's Pershings hit the beach again- their fourth wartime amphib landing. After 4 such jobs, they've gotten to be pretty good at it.
I believe LSTs came ashore after the first wave, which is what I was referring to. The DD Shermans were deployed from LCTs, which could carry four of the modified M4s. With a weight capacity of 150 tons, these vessels could hold perhaps three M26 tanks. IF a flotation screen had been developed for the bigger tank.
So I stand corrected. Adopting the Pershing would have meant 3/4 the tanks that actually hit the beach. I still don’t think the Pershing was ever modified to “swim,” but I could be wrong on that too!
Of course the US Army could have hit the beach with Shermans and unloaded Pershings for the drive inland one the beach was secure.