Well you don't HAVE to cut them down. You'll never know whether your hunch was correct unless you try. I'd think about the look, too, from the side. Take some side-on shots with the top taped on. if you like the tapered look, keep it.
The gofriller in chandlers book has a nice taper from 9" at the saddle to about 7" at the heel, and that's a carved back with no bend. Looks nice and it's a master bass ...
have you done any calculations of the relative volume of the upper and lower bouts compared with another model?
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