If you own a lathe have a look at the "metal spinning" process. It requires glowing the case to make the brass soft prior to work start and most probably also during work. The brass becomes hard very quickly during metal spinning.
But to hold such a case a very large lathe is required and you must machine a special chuck for exactly the 18-pr case size to hold it safely. Like@pzgr40 said I also think it's not worth the effort.
Another idea would be to use a Standard three jaw chuck and something like a support mounted steady rest with three rolls wich can be adusted in diameter. I think this would be the easier way and it's possible on a smaller lathe too. But it's still a lot of work for a 18-pr case.
Independent of which method is used the case will be longer after metal spinning and must be trimmed back to original length.
I once used metal spinning to produce a tapered brass fuze cap for an very rare anto balloon gun fuze. I used a old russian 23 mm case and shaped it as I needed.
So how have you got on so far with it up to know, looks like you are getting there so far.
Andy, just re read your post, looks like you are well on the way to getting rid of the flaring, I hope you were hitting the brass with a stroking motion toward the open end not just bashing at 90 deg to the axis. by drawing it forward you loose some of the extra metal into length that can be trimmed back to a marked line at the correct length. did it with a 120 bat case a long while ago and it came out ok