Your fired brass looks exactly like my friends WR Mauser's brass, before and after firing. It is very similar to an improved case. His rifle, a Westly Richards Mauser was never modified after leaving the factory. I believe that is what the brass is supposed to look like. The shoulder is virtually identical to a .416 Rigby shoulder. How about a picture of your factory round?

Will used to load for it using CH4D dies I believe and achieved 2,350fps to 2,400fps with 250gr. Barnes old style RN bullets. He did not load it hot as it has about 73gr. capactity, roughly 10gr. more than an '06 and is similar to an improved case.

Fired cases should go back into the chamber, in any rifle. If not, the chamber is not round or not straight. IT matters not what rifle or ctg. it is, a fired round MUST fit the chamber it was just fired in as brass shrinks .001" on average after expanding to fit and seal the chamber when fired. This shrinkage is what allows it to be extracted. if it didn't shrink after firing, you wouldn't get it out. Try turning the case and re-inserting it into the chamber. If at some point, it re-chambers, it has an out-of-round chamber.

Could it be that brass from one barrel won't chamber in the other, but will chamber in the barrel it's fired in? That could very well be the situation, ie; both chambers are not identical. Sized brass most certainly chamber.

Making your brass from .30/06 cases is quite feasible - they need to be necked up first - perhaps to .375" then sized back down to place the shoulder in the proper place for proper headspace.

To simily neck them up and fire, takes the chance of blowing the rifle up due to very much excessive headspace on an unaltered '06 case. The shoulder MUST be properly adjusted, as I noted. Re-forming the shoulder as noted, is called producing a 'false' shoulder.

This picture should explain what I said about necking up and then using the FL die, properly positioning the shoulder. The rifle I am altering brass for, is a 9.3x57 Husky. The rifle has .019" headspace - .007" is MAXIMuM CIP, .006" maximum SAAMI allowed for safety for any modern rifle.

You can actually see the difference in height of the shoulders betwen the simply necked up case and the formed case. As this 'newly' and properly formed brass perfectly fits the chamber, it will last for at least 30 firings.
The first case is a factory case. The second is a factory case merely necked up. The shoulder is too low (body too short) to fit the chamber properly with support between the shoulder of the case and the shoulder of the chamber.

The third case is a case necked up straight in one pass with a die I modified. The forth is a straightened case necked down in a 9.3x57 FL die set properly to make a shoulder in the proper location, so that there is a slight 'crush' fit when the bolt is closed.

This is the same thing you should do to your .30/06 brass before ever firing one in this rifle. With proper fitting brass, the chamber is perfect.