Will the Redding bushing dies fix all this?
When it comes to spending your money on a fix I'll bet there are many dies available.
But first, allow me to ask why you insist on sizing a case for a SAAMI chamber. You fired a case in your rifle then reloaded it. Now? It will not chamber without difficulty when closing the bolt.
I size cases for short chambers, WHY? When I cut a chamber I want to know the length of the chamber from the shoulder to the bolt face before I start, I want to know the length of the chamber while I am cutting the chamber. AND it comes in handy when I purchases a barrel or rifle that was chambered by someone that insist on short chambers and does not understand how threads function.
You fired a case, I will assume you were firing new factory ammo, if so you passed up a good opportunity to determine the length of ammo that will chamber in your rifle. You could have measured the distance from the shoulder to the case head, you could have measured the diameter of the case head above the extractor groove.
I believe other reloaders are going to insist you purchase a small base die. I have small base dies, I do not use the because they do not size the base of the case. It is the base of the die that is small not the base of the case. Then there is the shell holder, the deck height of the shell holder is .125" meaning the die can not size the base of the case.
I would suggest you use a feeler gage to raise the case head off of the shell holder, I would suggest you start with .005". The shim will increases the dies ability to shorten the length of the case and the shim will also increase the presses ability to overcome the cases ability to resist sizing.
I do not know what press you are using, it is possible your case is whipping your press and then there is your lube.
F. Guffey