mapping a warped space.

hey, I'm having a hard time solving this one.. I thoght maybe kangaroo can help..

I have a point inside a warped box and I'm trying to map that point so I can transfer it to another morphed box..

so once I know on which of the surfaces the point is.. I will have it's height.. and the u and v can be extracted from that specific surface...

so my question is.. out of all the possible surfaces ranging from bottom to top( every segmentation of the box edges gives 1 surface) like 0.5 is the iso curve in the middle of all 4 bounding surfaces.. and creates a surface.) which surface , and there is only one obviously, has the point on it?

I tried evolutionary solving for this asking for the smallest distance from the "closest point on surface" to the point I'm checking.. but only got to like 0.016

so this is not the correct mathematical way obviously.. there is a mathematical solution which I can't think of..

incluses is a video to explain.