Weaving deform to bowl

Dears, i have a weaving as you can see in the screenshot and i need to deform like a bowl, i tried a lot of tools like FLOW, FLOW ALONG SURFACE, BEND, ecc… but I didn’t get a good result.
File in the attachment

Please can you suggest some solution?
Thank you all

rhino.zip (17.3 MB)

Please give it a try with ShapeMap,

3dTexture.gh (107.1 KB)

WoW great! Nice solution, i realy apprecieted, thank you so much, i will try, stay tuned!