If you have cerrosafe, do a chamber cast and it should push the piece out with the cast.  I have used a wooden dowel slightly hammered it the chamber and pushed out with a cleaning rod at the range several times with my 25-20 Win.

I carry this tool that Jerry Hartwig showed me how to make that removes a stuck case next easily,

Before going through too much trouble, shove a bronze brush into the case from the chamber end, the try to pull the stuck brass out.  If it doesn’t work, just push the brush all the way out the muzzle and go to plan B.

JerryH, the brush trick usually works with bottleneck cases that have separated near the base, but I really am not sure how well it might work on a relatively straight case like a 25-20SS.  If it doesn’t work, I certainly don’t think one single brush stroke through the barrel will do any harm.  

I have separated case removers similar to the one pictured in an earlier post, and they always work well, but not everyone has them or the capability of making them.

I offer the idea as a tool in the tool bag to try if Joe cares to.

A .223 case extractor may also work on the SS case.  They are available from Brownell’s, and probably other vendors.  Here is a link: (You need to Login or Register to view media files and links)

I’ve pulled broken 40-82 cases with a tight wool chamber mop. I pushed it in and then pushed a tightly patched rod in from the muzzle to push it out. 
Cerrosafe as suggested earlier will work every time.

Take an 1/8” dia. Brass rod , grind 1 side so it tappers to nothing.
Push in chamber till it touches case and lightly tap with small hammer.  when it starts going under the case go a little further
And it will bulge the case moth , remove some pressure and should come right out with cleaning rod from muzzle. Did it many times
With a sharps 40-90 straight and it worked great all the time.
Very thin case mouths.

Joe,
For clarity on the cerrosafe process, I use a brass rod, - in your case it'll have to be around a 3/16" diameter one - a brazing rod from a welding supply shop is a good source.  I cut a cotton patch that when it's wrapped over the end of the rod fits the bore snug.  I then push this rod in from the muzzle end to within about a 1/4" of the case.  I leave this in place, even a wrap or two of black tap to hold it in place.  I heat my cerrosafe, make a paper funnel that just fits inside the chamber, a 1/4" to 3/8" past the rim.  Tape works to hold this in place also.  Pour your cerrosafe in the chamber and let it set up and cool down to room temp.  A couple of taps on the brass rod sticking out of the muzzle has always worked for me.  For a picky client, I wrapped the brass rod every six inches or so with a few wraps of black tape so the brass never contacts the bore.  For my rifles it doesn't matter.  I'm not that particular.
Hope this helps.
Greg

Good job Joe.  It was really in there.  I will have to try Greg’s paper funnel idea.  I usually make a mess. 
The first time I heard of using this technique was in the middle of a 2 hour relay at Tommy Mason’s range in Nine Mile Falls when Bruce Kirby pulled out a stick case piece from a competitor’s rifle so they could finish the match.