This seems like an obvious choice. It might not make perfect corners on the new dowel but I can't imagine people will be looking up at where this meets. Very easy to remove stock quickly and if you orient the dowel right you should be able to get nice flat surfaces. Other power sanders could work for this as well just maybe not an orbital one as easily.
This would be a cleaner and more precise option. If you were leaning towards hand tools this would be a good candidate. Clamp the dowel between two pieces of sacrificial wood. Better yet would be to take a block (or two) and cut a inch hole in it. Then the dowel will rest in that block with only the dowel to be remove exposed. Plane until just before the "block". A small block plane would work nice for this.
You don't mention how much need to be cut but if the ends don't need to be cut to far you might end up making the ends more tapered. That could work to your advantage giving a tighter fit.
I had though about chisels but was worried that they might try and walk along the grain and ruin the edges.
You might even be able to get away with a card scarper as well but I would not put this in front of the other options.
Update from pictures
Like the other I think that the original rib could still work in place. You should just be able to glue it back together with some clamps. The one thing I would do to try and reinforce it would be to drill a couple of holes across the break and fill each hole with a similar sized dowel. Glue those in there and I doubt it will break there again. I could not find a great picture put in concept this is have I meant
Just like the peg holds the tenon in the picture above a couple of small dowels can help hold your glue joint and give it some strength.
This is of course assuming the ends of the rib were not damaged as well.