use for lenz attribute LenZ =current("lenz") it will adjust first then become stable make X,y adjust to position, you have them set at a value, delete the = with Z, you could create a option to change its value or use =current("z")

I hate to throw another idea into the mix, especially as I don't have a specific way to do it in my head but, Could you link the data file to an image in sketchup itself so you can use it in a viewport in Layout. There are various plugins that can make links to external files and there may be something that works better for you. God knows if it would be any use, but it was a thought.

You could mark corners of the object on site before making a photo, just for help...In the case when there is no orthogonal lines, I would use that photo as watermark image in SU (under style). You can adjust your view of the model to match the watermark background, which stays fixed while rotating the view. Later on, you can use it in render application as background.