While I agree that it more than likely the case trimmer not trimming your case mouths square - The Lee trimmer does not go off the inside of the case. It spaces off of the holder that goes into your drill or the hand held trimmer. The pin that goes through the flash hole is what determines case length. I always de-burr the inside of the flash hole, as I too feel it aids in consistent ignition - But the burrs would have to be very big to effect your case length and especially your "tilting" problem. I think that the flash hole being off center would effect the case mouth squareness to some degree. You never said what cases you were trimming. Are they military cases? I found that some of them have flash holes that were obviously off center. With as much as you have said that the case mouth is off, the Lee trimmer would have to be a real odd angle, more than I have seen to date with mine. For a Lee trimmer to do a quality job, the flash hole needs to be in the center of the case, the case neck must not be over size and the neck must be in line with the center of the case body. If any one comes into play, you will get a case mouth that is not square with the case body. As much as you are talking, one or more must be way off. Are you talking about new cases or once fired cases. If they are new cases, you should full length size them before trimming to square the necks to the body. If they are once fired you need to full length size the pistol cases and at least neck size the rifle cases before trimming. If there is much play between the shaft of the Lee trimmer and the case mouth you could be tilting the trimmer to one side when you trim. As you can tell, I use a Lee trimmer for most of my trimming jobs. I also have a Lyman Acculine case trimmer. I only use it for the cases that I do not have or can not get a Lee trimmer for. I feel the Lee trimmer cuts the case mouths more square than the Lyman trimmer. Before you go through all of this, check to see if really is your case or the bullet not seating square. It could be a combination of both too. Good Luck and Good Shooting