I think you are better to go down the "abandon it" route Graham. The wood is almost in two pieces. The shake goes almost the entire length of the grain at the front and almost to the centre point, much lower down at the back. No amount of CA is going to keep that safe. There are methods of dealing with it - boring, pinning, stapling and so on, and if it was a priceless piece of irreplaceable burr I might be encouraging you to learn some new saving skills. But it isn't - it's a piece of run of the mill oak, and in this instance the need to keep your head and face intact outweighs the time involved and the risks associated with saving it.
In my opinion you would be better to get it off the lathe, get it on the bandsaw and re-purpose it I'm afraid