Another way is to restore the top, then to make a template from it, maybe with thick plywood, then to glue the ribs on the template, only at blocks, temporary, then to decide what to do with the back, then to restore the back and glue it on the ribs, then to remove the template and glue the top. this way you can widen (or not) the back to follow the top shape. Also, the top-ribs joint is usually flat, while the back is bent.
My two cents, good luck.
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