Huh. Usually when the tool starts cutting poorly, yeah, a new (sharp) one is called for. If your trimmer is leaving a big nasty burr even when trimming after every firing, then maybe the cutter on your trimmer needs looked at.
I had fits for a while with my Giraud - but only in one caliber/cartridge (308 Win). Turned out, I'd worn out one set of cutters on the triangular head. I *thought* I'd rotated the cutter, but I still got big nasty burrs. Eventually I figured out that yes, I had rotated the cutter, but I'd let things bang against each other in storage, and managed to screw up the edge on the second cutter - even though it was carbide. Finally just got a new cutter, and everything worked again. Oh, and I make damn sure to wrap the cutter in something before putting it back in the drawer.
Not sure if any of that applies even tangentially to your situation, but maybe. I just don't know that getting a carbide deburring / "outside chamfer" tool is going to be fixing whatever the underlying real issue is.
Good luck.