You don't need a mill or taper the mandrel.
You can even make a simple mandrel on the end of a piece of steel or aluminum bar stock by turning it to a tight slip fit to your bore (you can leave a shoulder on it for registration), Affix the part to the mandrel with Cyanoacrylate Adhesive (Super-glue). Machine the part then use heat to remove the part. Use some sort of coolant so you don overheat the part and release it prematurely while turning.
You can make an expanding mandrel like the one in the link, but it isn't necessary for a one off part. Basically, it's a flathead screw through the center in a countersunk hole, when tightened it pushes the segments outward to grip the part. You can cut the slots with a bandsaw or even a hacksaw.