[Geoff Bacon]

I don't really see a major issue here

Create each song as a separate entity i.e. only one song per name

Basically, you can put the songs you want into small setlists  e.g. A+B+C, A+B+D etc. (you can use the "+" character in the set list name)

When creating a new setlist for a gig, just use the New option to create the empty list. You might ;like to add a space character to the name of this setlist so that it appears at the top of the page (assuming alphabetic sorting)

Then on the Setlists tabs, long press the first "short" set list you want to add e.g. A+B+D and press the "three vertical dots" at the top right of the screen and select "Add to Setlist".
Repeat for any other small setlists you want to add (they will get added to the end of the list you are creating)

Alternatively, you could have larger "small" setlists and edit the new setlist to remove items you don't want in the newly created setlist
If necessary, you can also use the edit mechanism to add songs that don't fit into a predefined "small" setlist

After the gig/performance, you can either delete the full setlist (leaving just the small setlists) or, if you added a space to the start of the name, rename it without the space so that it moves to the correct position on the setlist page. Including the date as specified  by tmj100 also helps maintain an order to the setlists  i.e. yyyy-mm-dd  2019-11-25  (using 2019-Nov-25 will not aid showing the items in date order)

There are probably other ways to achieve what you are trying to do but, not knowing your exact requirements, I guess you'll just have to experiment to get the result you want

Cheers
Geoff