At the risk of sounding totally stupid and unqualified; the bore of a firearm barrel isn't tapered.... right?
My closest mandrel is .2185 on the small end and .2205 on the large end with the tapered part being approx 3 inches long and overall length is 3.75.
The ends are smaller and have a flat for the driving dog.
smallest mandrel I have is .1245 small and .126 large end. Taper on it is 1.9 inch long.
It's a very slight taper and a part that fits wedges on tightly.
It's very easy to miss the size and your part almost tightens up, In that case I have used superglue or built my own mandrel to fit.
I built my first mandrel on my lathe. So don't be afraid to do that.
No taper in barrels.
Range rods I think used to be built with slight taper changing to more taper to wedge in the barrel.
Now (pacific tool) is building them with replaceable bushings on the end. You find the correct bushing that fits your barrel and it goes
on the end of the rod and when pushed in it bottoms on a slight taper so is centered in the bore.
If you use a mandrel without superglue (or maybe even with) your cutting pressure should be in the direction of forcing the part
farther onto the taper as opposed to pushing it off the taper.
Purchased mandrels are hardened and may even be HSS . The part is driven onto the mandrel with a deadblow hammer.
Usually I'm driving the mandrel into the part actually.