I checked in with our Hardware Specialists, and unfortunately there's not a way to rearrange the pages on the Register. You'd have to delete the old page and then create a new one if you wanted them to show in a different order.
This is a feature we have long wanted as well. Just super time consuming and annoying that you can't just rearrange the order of the pages once they are created. Deleting and restarting a page doesn't fix it, because if you need that page between two other pages, now you have to delete all three, then add them all back in, in the right order. Seems like it would be a simple fix to make it so you can reorder the pages as well as the items.
Definitely hear you on that one, and happy to pass the feedback to the team. They'll do make changes based on feedback like this, and we'll hopefully see progress on the request in the future.
Any update - seems like easy to implement and should have been there in the first place. We are often changing these items and deleting and redoing is not acceptable in terms of functionality.