As you noticed, you can only add lists to the bottom of a script.
The best way to organise your lists in the TinkerList script?
There are two possibilities:
From the side-bar
One is reordering lists from the sidebar (where you have the folder structure). Here you can see the different lists inside of a script and reorganise them by dragging and dropping them in the right order:
Collapse lists
Another way is by collapsing the lists inside of the script to have a more compact overview. You can reorder the lists by dragging and dropping them in the right order: