I am in the habit of cloning pages to speed up the entry of new pages. I do this because the format of my writing follows a set pattern as the site in question is designed to be a reference site for others. However if I clone an existing page, e.g. one created prior to my changing the layout for new pages, the cloning process copies the "old" layout and associates the new page with the old layout - e.g. "Layout (Nodes with Images)" is copied but all my new content uses "Layout (Pages with Paragraphs)".
I'd like to use the new layout with the cloned content but I cannot work out how to do this... Any suggestions?
Yes, I'm still somewhat confused about your setup and what you are after, I admit.
If all content of a certain type is showing up on the wrong layout, you may just need to adjust the visibility conditions and/or the order of your layouts to make sure the right layout is selected.
If you need to clone certain content from one type to another to make sure the right layout is selected (and you don't want to lose data on fields from the initial content type), you may need to add those same fields to the second content type so that the field data has somewhere to go when you convert.
It's a little bit difficult to grasp what you're working with and what you are intending to do, so take my suggestions with a grain of salt.