I would honestly use the image mapper. A pattern would be possible, although getting the parameters for the spiral just right would be a little tough, but especially when it comes to mapping both sides of it.
Personally, I would try two things:
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Using the photo mapper and clicking on the “hot spot” where the light is hitting the white background rather than on the LED itself, so that the layout of the lights is more evenly spread out and more accurately reflects where the light coming from it will be visible, rather than the location of the LED. This should really help you see the entirety of a 2D pattern across the whole area of the spiral. Otherwise, the LEDs on opposing sides of the spiral will have almost the same X and Y coordinates.
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If that doesn’t look good, using the photo mapper and clicking as close as possible to the actual LEDs
I do wonder how much the “coolness” of the spiral will be lost by turning it into a standard 2D map, but I think the fact that the LED strip blocks light and keeps it contained will end up creating interesting patterns anyway, even when running a standard 2D pattern on it.