Printing to be viewed at 45deg
Your model is quite clear, although the question is less so. You ask if increasing the height of the image in the background to 200% is the best way.

The best way for what purpose?

If your objective is to maintain an approximation of the original image, the number would not be 200%. 

Consider that the red line extends below the forward lip of the shadowbox. Your measurement point should begin at the intersection of the orange triangle and the red line. From that point, the correct calculation is to use the square root of two times the original height, presuming the 45° mentioned in the question. 

For angles other than 45° it is necessary to use a bit of trigonometry.