I have a set of RCBS carbide dies for .38 special/.357 mag. I don't use the one to flair/bell the mouth because I do this with the die on my powder measure. Different presses equal different setups. The cases using my dies come out sized small enough there is no way I could push a bullet even .357 jacketed one in by hand even after seating and before adding the crimp. A 9 mm bullet is another story. I could press a .355 bullet into the case by hand. It would take a bit of effort but I can do it. I don't have many lead bullets available to try those. Those shinny bullets you have are probably hard cast.
It really does sound like you may have some bullets that got sized to the wrong diameter. Things like this do happen.
I don't use calipers for .38 special or .357 mag. loading. The bullet tells me where I need to crimp at in most cases. It is quite different when I load 9 mm and .45 apc. I have been loading Speer and Montana Gold bullets lately and have never run into the problem you seem to be having.
You would have to put a flair/bell in the case mouth pretty deep to have a loose bullet in it if the bullet was the correct size. The way the RCBS dies are made it would be difficult to do that and not have problems getting the case to enter the seating die. I doubt too much flair/bell is the problem so we are back to a bullet problem.