It is fine to put bore butter in your barrel for storage, but a sabot is made to shoot over a clean dry surface. If you don't get all the bore butter out before you shoot, it will make your sabots very inaccurate.
I would take a piece of cotton and run it down your CLEAN DRY barrel. After running it through, look down the barrel and see if your barrel has any cotton sticking to the inside of the barrel. If you see cotton sticking to it, you may need to polish the riflings with a little bore polish of some sort. Sometimes if you buy a new inline, they will have burrs on the riflings. There is nothing wrong with it, and they will eventually disappear with enough shooting, but you can speed the process up by polishing the barrel with a light abrasive polish, about 100 strokes will probably do the trick.
This may be why you are getting plastic in your barrel from the little jags in the riflings, cutting into the plastic.
I use NOVUS Plastic polish for this when I get a new rifle. It is light enough abrasive to take out the burrs, but not harsh enough to hurt the riflings.