Looks good - I'be made a few acrylic & Corian stoppers, but I generally prefer wood. I can knock out about 3 wood stoppers in the time it takes me to make 1 from acrylic & the material is much cheaper.
I'm not sure what you mean by the end being unstable - do you mean that the threaded piece is a little loose? I drill my holes a little undersized from what is generally called for (I usually use a 9/32" bit) then tap it before threading the blank on a mandrel. With Corian or acrylic, I use a 5/16" bit but still cut threads with a tap.
If the finished hole is a little large, you can always use epoxy to hold the stopper in tightly.