If the cases can be primed on a different machine, the problem is not with the cases. Do not alter the cases.
Reaming new cases that do not have crimps and that can accept primers??? I can see running a uniformer into them to groom the bottom of the pocket, but reaming the case to enlarge the diameter of the pocket could very easily result in a bunch of useless cases.
I have one of the old RCBS hand primer tools that I have used for decades and have never used one of the newer universal versions. I can't, therefore, give exact instructions. There must be, however, parts that are specific for large primers and some that are specific for small primers. Are you doing something like trying to mix up large and small primer parts? Doing something like trying to use a large priming rod for small primers would not work on my machine and probably would not work on your machine. One fellow I know had problems with his priming machine denting the primers. All he had to do was turn the priming rod around so the flat end of the rod contacted the primer rather than the round end of the rod. You might need to give RCBS a call if you can not get it working properly.