Need better mould result

[Contours]

I have an image that I need to overlay onto another image of a slightly different "angle of perspective".

I've been trying to use the mould tool, but its pixel-level processing is producing an unusable result (see before/after, below). Plus, I having trouble getting the precise dimensions I need. I spend a lot of time trying to skew the image (shear + mould) and then move the image to get it back to the right place ... and then having to change the shape once again.

Is there a better way? Is there some kind of "dimension change" tool or method?

Thanks in advance for any help. (I'm using Pro X9.)