I make game calls which are a little bigger than pens but basically the same. I have sanded all the way down to 600 and have had no such issues with any wood or other materials.
You may be sanding too fast or with too much pressure causing the wood to burn. Try slowing down the lathe while sanding and not applying as much pressure.
You should be able to get an extremely smooth surface with no sanding marks at all.
I use several different finishes including tung oil, laquer, shellac, etc and am able to get a glass smooth finish.
I hope this helps, and by all means please feel free to contact me if it doesn't or you still have questions.