When I use my chamber checker , almost all the rounds do not drop in flush. I believe that maybe the bulge of the .356 diameter may be the reason.
To be clear, this is a case gauge and not the barrel from your gun? I had the problem with my Wilson 45acp case gauge. These are made to minimum specs and gun barrel chambers are typically bigger to be more reliable. When I tried mine, only the occasional lead boolit handload would make it flush in the gauge. When I pulled the barrel out of my gun, they all did the plunk test fine. Try using your barrel as a gauge.
You didn't state the gun you have, kinda important.