I think if you can be assured of a good glue joint them a veneer doubling would be strongest especially if the rib is badly damaged. So effectively you have a new rib but with the old rib becoming a decorative veneer itself. And if you're going to replace the linings then the doubling can go edge to edge.
But getting a good glue joint on such a large surfaces is tricky, it is much more practical to fit and clamp softwood strips and/or linen Ã* la
Bollbach