Only a small update to show that I've managed to cut the new oak strut to fit and support the landing
I started off by attempting to tenon-saw my way through the beam, but after 30 minutes gave up in favour of a chainsaw to take most of the meat out of it, and a chisel and plane to fine-tune the fit.
You can see it compared to the strut that it's replacing (above, left).
And here's a nice arty shot of the shake which is running down it's length. Lovely.