Need a small punch die made

A way to make that shape.
For the punch start with a round bar in the lathe. turn it to .808 dia at the end and taper it about 20°. Now tilt it at about 15° in the mill and cut the big end flat. this will give you the cutting end of the punch in an ellipse that is .808 x .838. now take that part and place the cutting edge down flat and mill the other end parallel to the first cut and you will have a nice punch with about 5° of relief.

Now do the same for the die, start with a bored hole with the 20° taper getting bigger from the .808 dia. Tilt it on the mill to make the elliptical hole then flip it to make it back into a plate.

If you are using soft brass you will probably get away without heat treat. If it is a harder brass you may want to heat it up to a dull red and drop in oil.

Make a round punch for the holes and punch them first, have a pin slightly smaller than the hole to use a a centering guide to punch the ovel.

This will not make a perfect ellipse, but it will be within a couple thou.
 
Another option.
Since there is only .020 difference between the 2 axis, you couls also just make it oval. It is fairly easy to machine an oval hole and an oval punch.

Not knowing just how precise this needs to be or its intended use makes it hard to come up with more ideas.

At a place I used to work at we used a wire EDM to make punch die sets. The wire was set at about a 2° angle and the shape cut out, flip the slug over and it will be about perfect fit for the punch and die. This only works for symmetrical shapes.
 
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