CJF,
I suspect yours also has chambers for the "D" version. Your "fix" is very close to one of the ways to deal with the problem. Some just run current "N" version ammo far enough into a 38-55 file trim die that it will chamber. The 38-55 head size is a few thousandths smaller than the 9.3s, but the bullet is larger. This allows the bullet to pass through the die and size the body farther back. A little lubricant is necessary and size it only enough to chamber. If you set the die correctly, it should take less time than the system you use now. You can do the same thing with a 38-55 FL sizing die, if it is the type that has the de-priming assembly in a separate threaded bushing instead of directly screwing into the top of the die body. Removing the threaded bushing will allow the bullet and part of the case to pass through. Of course, if you don't already have 38-55 dies you might not find changing your procedure worthwhile. I'm sure you have already found out that you only need to do it once; you can reload them after firing them in the normal manner using normal loading dies. You mentioned that your rifle also has tight barrels. I have found that .358-.359" groove diameters are very common, which is handy.
Mike