Have you heard from them that they need the pages shuffled? It's normally their job to do the imposition before printing.
If you have to impose it yourself, I think I'd creat a two-page, non-facing file with three times the page width and set three columns, then place the pages from the original file in the order you want them. Doing it that way gives you only one file that needs to be edited when changes are required. You just update the links in the second file.