I will try to sum this thing up. A case fired in a rifle will go back in the same rifle. If the fired case is full length resized it should easily go back into the rifle. In this case it didn't, so something is wrong.
Proper full length resizing will not prevent it from going in, so something has fouled up in the sizing. The op now says the sized cases, without loading them, will not go back, proving the sizing is at fault.
If the case is properly lubricated, which means sparingly lubed with a good lubricant, even partial sizing will not prevent it from going in the chamber. I think what is happening has already been mentioned. I think the necks are dry inside and when the inside neck sizer is pulled out, the neck stretches out a bit. The solution is to lightly lubricate the inside of the necks and the problem should be solved. One way of doing this, without danger of lube in the powder, is to brush out the neck with a bronze brush. I have a brush on a handle and just give it a turn in the neck. This alone should do it, but better is to lightly lubricate the brush, so a minute amount of lubricant goes on the inner neck.
However, there is a tool that will end all problems of the loaded round not going into the chamber, and it is a mystery to me, why it is not used by more reloaders. I am referring to a trim die, made by RCBS, for one, that is designed to go into your press, just like any other die. It is a full length resizing die, with a glass hard, flat top. Push your empty case full into this, then file off any that protrudes out the top. The top is so hard that it will not harm a file, so just file the neck down smooth with the die. By the way, this should end all those threads we read about where are not getting the case length to the exact thousands of an inch. In fact, no need to measure the case at all. File it flat with the top of the die and it is right length.
Now, this trim die serves another purpose, which in the case of all the trouble described here, will completely eliminate it and let the case slide into the chamber. A fully loaded cartridge can be safely pushed into the trim die. There is just a hole surrounding where the primer goes, so it creates no danger in sizing the loaded round. The loaded round comes out fully resized, whether if formerly had bumps or stretches, around the shoulder, or anywhere else.
I have an RCBS trim die in 243. If people have never heard of it, I could take a picture of it, but it should show up in the RCBS site.
