How do I transform the 4 points A B C D to 1 2 3 4 respectively so that the individual planes AB, BC, CD and DA are mapped and stretched evenly across into 1-2, 2-3, 3-4 and 4-1?
I guess you ae out of luck in Photoshop. Normal warp is useless, you cannot get the edges and corners both right (tried), Distort in pieces breaks the image to displaced pieces (tried), Puppet warp needs a half hundred nails at edges and they still look out jagged (tried). A math transformation would do it, but that needs a programmer which I'm not.
Something quite nearly right is available with visual tools in Affinity Photo. It's Warp Mesh is incredibly loyal. Here the wanted area is made rectangular. It's not a big deal to stretch it bigger.
The same should be possible in Illustrator (=Envelope distort with mesh)
BTW. You did not specify how evenly it must be made. You should declare upper limits for local stretch and rotation somehow. Warping this way surely doesn't scale lines AB and BC linearly. Math transform is the only way have exact control.