Distorting vertical line gradients

Hi all,

I'm having a little problem with something that I believe should be quite simple. I'm trying to create a deck chair's striped canvas, which tapers from the top to the bottom of the shape. I need the stripes inside of the shape to taper also, meaning that the width at the top of the stripe will be slightly wider than its width at the bottom.

I had been messing about with envelope distort but this is just affecting the shape and using it as a clipping mask to the unaffected striped gradient behind.

Hope I've made that understandable.

Please help!

Thanks,
Will