It seems I have misunderstood what you're looking for. The "spider" I have in mind fits inside the chuck jaws for working with short stock. I ran down the drawings for the post above. And was surprised at something so simple could be so hard.
The one I made is so crude it looks like it won't work. But it does, well enough for what I do, anyway. Mine is three point, I'm sure a four point would be easier. Just a center finder on most any machinist's scale. The three point involved making a disposable insert to achieve a center divot. Then swing the radius to get sixths, taking every other one to mark the stock. With a four point spider, if the tips of the setscrews will make up to the stock, it can be centered. Might take some adjusting, but doable.
What I want is the insert for a three jaw chuck. It looks doable, but for the small sizes I need, it will be sorta flimsy. I'm still studying on how small I can get and it hold up.
Bottom line, make what you need out of a piece of pipe and some set screws. As long as the set screws meet in the middle it will do the job. When you get a dividing head, make a pretty one. If you ever do, those things are 'spensive,
Bill Hudson