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I guess it depends on how accurate you want the calculation to be. I see it as you have two options...
Hand calculation route: You know you have 120,000 Btuh to work with and you know your internal peak load. You can set your solar heat gain proportional to your floor square footage and then write an iterative solver in Matlab or something to find floor area.
Energy model route: You could automate E+ runs where you are scaling the floor area trying to minimize unmet hours.