There are two stanchions at the back of the boat that were meeting the deck on the curve. They had plywood feet, to match the shape, but had rotten through. This allowed the stanchion to move, the rail to move, and led to damage at the corners where the rails met.
Once that was complete, I removed all the railings. They were sanded back using various sandpaper weights, finishing with 600 grit. It turns out that they are Mahogany... I decided to try Deks Oilje, soaking them with Deks Oilje 1, then finishing with 6 coats of Deks Oilje 2 (sanding between coats 5 & 6). Here are the before, during and after shots:
