Interesting:
Taking a rather broad swing with respect to the requirements......
To use Tiermakers' "Hats" as an example - the songs would be the hats and you would move the songs up and down the ranking list. Something like that correct?
What format is used for the submitted ranked songs? How many entries/submissions are you working with? How often are the rankings changed?
(Are you live streaming your display and your audience watching the song list drags and drops?)
Are you familiar with Microsoft's "Sticky Notes"?
Just FYI:
https://docs.microsoft.com/en-us/windows-insider/apps/sticky-notes
The song or songs could be put in Sticky Notes, displayed and subsequently dragged and placed on a desktop for display. And mostly a manual process in both ranking placement and dragging/dropping. Not automated and perhaps a bit cumbersome.
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And there is another option you may find interesting/applicable. Especially with respect to the "satisfying visual" requirement.
Basically as I understand the process you are just creating icons that can be edited and dragged about.
Are you familiar with Scratch (MIT)? Free.
https://sip.scratch.mit.edu/scratchathome/
Technically used to teach coding; however, you can do quite a bit with Scratch. Create "song" sprites and move them about. (Could play the song as well...)
Without revealing any personally identifiable information would you be able to post some images that will help with understanding more about the requirements.
Use imgur
https://imgur.com/
Feel free to correct any errors in my understanding of the requirements.