I recently bought a second hand short shank Yamaha mouthpiece to use with my Besson Sovereign cornet. The mouthpiece doesn't seem to fit and wobbles. I have tried it in a couple of other sovereigns and had the same result. Do some brands just not fit?
I had this problem with an old Sovereign. Then after it was ultrasonically cleaned as part of a service the mouthpiece fitted. It seems there was a build up of mineral deposits inside the receiver around where there was a gap where the Wick had been sitting in it. However, some of the later sovereigns have problems with the mouthpiece inserting too far and hitting the point where it merges into the leadpipe. This may be the problem you are having.