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Re: Adding woodwork below
I don't know the answer to that. I'm not an expert, but I know some boats have a thwartwise beam under the mast support, and attaching to this would seem to eliminate the concern over making an inflexible hard spot--it's already hard there.
Though you don't know the reverse--how the strains that the mast & rig places on that deck structure may affect the joint you create.
My unscientific sense of it is that whatever you do within reason probably won't have very great structural consequences one way or another.