In that odd scale, I think your only option is scratchbuilding with styrene strip and shaped stock - but since the launchers are basically long rectangles, that should be doable. Get the approximate dimensions from photos of the Missouri in that timeframe. Make a "test" launcher out of styrene and put in on the model where it belongs to see if it looks about right, then duplicate as necessary.
That's what I've had to do updating my USS Enterprise to her current configuration, since the ancient Revell kit depicts her as launched. I am not one of these rentetive types that has to get blueprints and do the math to get the measurements down to millimeters - I get as many photos as I can, rough out the shape in styrene sheet or strip, and the fine tune it until the piece looks "right" to my eye. So far the two sponsons I've built look pretty good for a first effort.