Custom distortion of UVs on mesh

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I am trying to alter the UVs on a curved wall mesh so that the left and right edges are increasingly stretched horizontally.
The attached should make this clear.
In the bottom half you can see the green box (which is a rendertexture on the curved wall mesh) is stretched horizontally in the center and appears 'squished' towards the left and right sides. From the viewpoint of the camera it has to appear as a consistent square regardless of where it is poistioned left to right.
The top half shows the capture setup with a Ortho Projection camera centered left to right in the curved wall mesh.
How can I alter the UVs on this mesh to get my intended result?

Attachments:
UV_map_issue.JPG (70.8 KB)

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