Nice mod/repair.
I've made a similar knob before by drilling but instead of turning it on the lathe, I just used a hole saw to cut out it out after drilling the 4 indentions. Also, I rarely chisel out the the hex hole. It seems like a I always wind up with a wonky fit when I do. I simply drill a countersunk hole that is just slightly smaller than the hex shape (the hole diameter is about the same as the wrench size) and simply press it in so that the corners bite into the wood. A few drops of CA glue or epoxy ensures it doesn't come out.
--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.