I’m pretty sure there is an option (per user) to change the page’s layout to single column, and then moving the block around to match the order you require. This option can be found on top of the page, accessible from the tab Screen options.
Note that, as this is on a per-user basis, you would have to do the change for everyone manually.
EDIT: As this solution won’t fit OP’s requirements, I would suggest the verification of the way the $.append() method is used. As described in the docs (http://api.jquery.com/append/):
If an element selected this way is inserted into a single location elsewhere in the DOM, it will be moved into the target (not cloned).
[…]
Important: If there is more than one target element, however, cloned copies of the inserted element will be created for each target except for the last one.
The cloning would mean the previously attached event handlers would not be bound on the new elements, rendering the input/buttons useless. Make sure you only move the container around to avoid element cloning.
Also see this thread on how to use the $.detach() function: https://stackoverflow.com/a/29462003/7392929