You can try duplicating the fingering articulations and ordering them in reverse.

Very interesting! I'll give it a shot

George, your suggestion worked, thank you.  But I'm having a terrible time saving my settings.  When I save the document, it only saves the "reverse" articulations I actually used, not all the ones I created.  So I recreated them all, and tried saving to a library.  When I load the library, the new articulations appear at the very end of the list, not where I moved them, and not in the reverse order that I had created.  Any idea why this is happening?

From how I understand Finale works, it should save everything you have created in the file. Not sure why things are not saving for you. Perhaps you are trying to copy the music into a blank document? That's the only thing I can think of where only the used articulations/expressions get carried over.

Regarding libraries, that is mostly expected behavior from what I understand—it should appear on the bottom. Not sure why the order is not maintained, though. It seems the best thing in this situation might be to setup a template file for future use.

https://usermanuals.finalemusic.com/FinaleWin/Content/Finale/ht-templates.htm?Highlight=templates

George, thanks for the link; I’ll see see if a template will work

What I've learned:

1) I had said that when I saved the articulations to a library, it put the dupes I created at the end of the library.  Not so; the document I was working on had been created in Finale 2010.  I thought that when, as a test, I created a new document with the setup wizard using a single instrument with the Engraved document style.  I created the dupllicate articulations and saved the document.  When I closed and re-opened the document, I saw what I thought were my dupes at the end (1-2-3-4-5) but it turns out they have been added to the default for Finale 26, most likely for this very reason, to enable reverse order double stop fingering.  It was easier to choose the correct finger when I had grouped them together (0-1-2-3-4-5-4-3-2-1--0), but it still works. 

2) Finale doesn't save a duplicate articulation in a document if it is an exact duplicate; at least one thing in the definition has to be different. In my case I have checked "Always place outside staff", and the "avoid staff lines" is redundant. So in the duplicates, I unchecked that box, and now the dupes are saved with the order I created.

And I can save these articulations in a library or template.