Try converting it to edit poly.

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The secret of creativity is knowing how to hide your sources.
-Albert Einstein

Turbosmooth will cause artifacts unless the whole thing is quads.

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I think you can get away with n-gons as long as your faces are all consistant sizes. Try dividing up your shape a bit more.

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You get the weird shapes because the polygons at the ends have so many edges. this is an annoying issue especially when you want nice bubbly text or something but the only way around it is to cut up the polygons carefully so they smooth properly.
Short of cutting up the beveled shape and getting very confusing results I'd probably approach Like this.

1. Create a plane with enough segments so you can describe the shape in a rough way, moving around the vertices (perhaps use a shape to trace over).
2. then add a shell modifier, collapse the stack (to editable poly) then select all the edges you want to remain sharp.
3. hit extrude and make height zero and make the width quite tight, depending on how beveled you want it.
4. Then you may have to clean up any corners which can be a bit of a puzzle trying to make them all quads.
5. then add the turbosmooth.

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