What if you create a repeater in the theme options.
It has title, description, link etc. But you add another column for post object. This is then a multiselect and allows the user to select which page that row should appear on. I’d set it to return the post ID
Your code then needs a line in your repeater which gets the current page ID and compares it to the row post object IDs. If it matches, show the content.
Would that work?