I've turned smaller punches (Ø1.5"-Ø3") and will admit that you will go through inserts. I can't imagine turning a Ø22" bar. And 3" of stock is pure insanity.
If it's a thinner disk, under 5" thick, I'd tell you to send the thing out to a water jet house and have a good portion of the stock roughed off there. Depending on the geometry, they might be able to rough it completely for a reasonable cost. If you need exact sizes and smooth surfaces prior to heat treatment, you can run skim cuts on the part when it comes back in.
If your required hardness is less than 65 HRC, I'd recommend heat treating the piece in a vacuum furnace to minimize distortion. Thicker pieces will likely need an oil quench, which may be why your heat treater wants 1/8" stock all over.
Tight tolerances post-heat treat will likely need to be ground as was mentioned prior.