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With the success of the Redstone Trident* in the early 50s, Convair's B-36 deal with the USAF gets cancelled (or severely cut back) and they're left with a big hole in their pocket.
Then one bright spark suggests they copy the concept behind the Avro Lancastrian and turn the B-36 into a passenger transport. They remove the military equipment, bomb-doors (which has the effect of pressurising the cabin), and the outer two engines from the design, and fill the fusilage with 40 tons of passenger ameanities. The Convair-636 is marketed as a transocianic 100+ passenger airliner. ITTL the Boeing 377 probably does get built and is competition.
It is successful? Or at least as successful as the Boeing-377?
*RT consists of three stretched redstones with cross-feed and better fuel. Or a very early model Falcon-Heavy if you want to think of it that way. This ideas were around at the time, and the math works out. ITTL America never worries about a missile gap.
[edit: Ops! The B-36 is of course a Convair project, not a Boeing one. Thanks Archibald]