In PowerPoint, how can you match an object's 3d perspective to that of a static image?

Question

My question is easiest to illustrate with an example.

I work with early-stage startups, so often make PowerPoint "mock-ups" of what software will look like when displayed on a computer screen. I start with a transparency of a computer screen or tablet, and use PowerPoint's 3d perspective tools to get my mock-up to match the angle.

A picture might make this clearer.

Getting the perspective to match is a lot of trial-and-error, and the result never looks quite right. Is there a "proper" way to do this? Is there a way to calculate the proper rotation values, rather than approach by trial-and-error?

Answer 1

Providing an answer to my own question, so that that my solution is documented for future readers.

Following a suggestion in the comments, I pulled up Pixlr and used the free transform tool there to match the frame perspective. I then exported everything back into my PPT, as a PNG with transparent background.

It had never occurred to me to do part of this outside PPT and then re-import. But it was really much faster (seconds!) and the result was far better than using PPT 3d effects for this...