Creating contoured stripes in Illustartor

I'm trying to do an Uncle Sam hat with vertical red, white and blue strips, and I can't figure out how to do that in Illustrator.  Is there a way to do it with on overall shape for the top part of that and then create th stripes with meshes or gradients? Meshes of course refuse to create sections which follow the contours of irregular shapes, and I don't know how to create a contour gradient.

I don't have any experience with Illustrator's 3D functions, but would a wire frame view help in this regard. (Speaking of which, how do I convert a surface to wire frame view?).

Here's my ai file.   http://www.discretedata.com/Ex-Ex/Uncle%20Sam%20Hat.ai

Thanks for any and all,

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