It might not require as much patience as you think.

I covered my foam core board with tissue paper and drew circles and lines on it, to guide the placement of the swizzle sticks. Then I played with the arrangement, until I was happy with it. Then use a needle and nylon thread to stitch the swizzles onto the board. I also taped the thread, on the back of the board, to make sure it didn't start to sag. Then tear off the tissue paper

It was laying flat, in this picture, with the chip just sitting on it. I actually glued a silver strike in the middle.