Just got back. Sorry for the delay.
So, copying and pasting actually is working just fine between your documents. The problem is that what you copied and pasted didn’t end up on the paper because you are copying from a large piece of paper to a much smaller one. In LayOut, pasting is always a paste in place operation. the “place” is always referenced from the sheet origin which is always the upper left corner. If you zoom back enough you can see the model viewport.
If you need to create two different documents on different size paper like you’re doing, you’re best off to either start the second file new by sending the SKP file to LayOut or using File>Insert in LayOut. If you must copy from one document to another, I would suggest starting on the smaller paper size and copying to the larger one. If you copy and paste from one document to the other, make sure you update the references in Document SetUp to have the proper links to the original files. Don’t leave links to temporary files which is what copying to the clipboard creates. If you are copying images or text files or spreadsheets, the same thing applies. You don’t want to see references pointing to temporary files.
As for the multiple page sizes, another possible workflow would be to create the document on the largest paper size and export it to PDF. Then when printing, print it on the smaller paper size.
By the way, I noticed that your scenes for your viewports show as modified. This is not a good practice because you are breaking the link to the scenes in the original SketchUp file which will create problems for you. More on that later.