You don’t have to extrude the ring. You just have to press it in as far as you need to get the size and shape you want. This is the reason for the witness lines on the pushers. You can take notes on what line will give you a certain size for a type of coin. You should be able to get a max size of 20+.
You can flip the ring over and press reed side down for your last push to get a straight wall. For example, if your target size is 12, push down reed side up until you get a size 13 or so, flip over and press reed side down until you get size 12, take notes on your witness lines for repeat sizes in the future, I actually don’t use the lines myself. With enough time you just get  a feel for it.
I actually only us the swede die to about 2 sizes over my target size then finish in the 17 and 25 degree dies. I like that look, a soft round.