I’ve never had any bad after tastes in my mouth. Actually with all the blends I’ve smoked, combined with my smoking and cleaning styles, I have no after tastes at all in my mouth.
I’m not sure if it was mentioned, but for me personally, I found the blends have a lot to do with this.
Keep pipes nice and clean
Dry out the tobacco fairly crisp
Pack lightly
Sip slowly and don’t worry about keeping the pipe lit
To much fire/heat and constantly trying to keep the pipe lit, could be a big culprit.
Try changing to different styles/blends, and pipe habits of preparation, smoking and cleaning...
Less fire/heat and the occasional small slow sips will lead to better overall mouthfeel taste.