sorting posts in a different way

I have a situation that I can not figure out.

I am using categories to set up a database-style section of my website.
The URL is https://www.frogstandrecords.com/licensingnew

Here is what I need to achieve:
I created a whole bunch of categories for different genres of music (listed on the sidebar). I am creating a single post with a music player for each song. I am then placing these songs in whatever genres apply. Most of these posts are in several categories at a time.
I need to find a way to determine the order of posts in each category.
For example, if the song “Pluton” is in both the female vocal category AND the dreamy category, I need it to be the first post on the dreamy cat and maybe the 10th in the female vocal cat.

I thought this system of making a post for each song would be convenient and easy to maintain. Then I encountered this problem, and I can’t solve it!
Does anyone have a solution?