Drag and Drop Help Needed

It doesn't look like that template is editable in any practical manner. The line numbers could be modified, but the rest seems to be linked to external resources. Sorry.

Other than using that built-in solution, you are rather limited.  The normal drag & drop cannot be made to start in a "dropped" state, which is why things appeared to stack; nothing starts as dropped in a target. In any case, when another item is dropped over an existing drop state, the original returns to its non-dropped state and starting position. The items will never swap positions the way you desire.

This may be too much but: If you are JavaScript savvy, you could look at incorporating an H5P module like https://h5p.org/content-types/sort-the-paragraphs .  The options here are to set it up on an external server and embed the content into your slide, or use a packaging utility to include all the content with your Storyline project, which you then can display on you slide as you see fit. Out of the box, there is still no direct style customization, but It seems more likely that this could be easily styled via some script. The H5P results are usually transferred via xAPI.