So I think I've sussed it out...
I remembered past problems I have had that were similar, with the app crashing randomly and they turned out to be when there was too many resources being loaded into memory. And were fixed by creating another Atlas.
I thought maybe the scene that the sharing extension is switching back to from Facebook isn't being loaded in time to execute the rest of the Sharing Extension code after the message has been shared. So I created new scenes that are used only when the extension is being used and put them in their own Atlas with only a background image for each. This was so each scene used by the sharing extension would load almost instantly, and hopefully would lead to the scene being loaded up in time for the extension switching between the Facebook App and the Scene it came from
I've tested it half a dozen times and it appears to be working perfectly now.