Further troubleshooting. In the other user account, where OpenLP 3.1.2 launched successfully, I replaced that ~/Library/Application Support/openlp folder with the one from my user account, where OpenLP 3.1.2 hangs unless launched from the command line. First time I opened OpenLP after swapping out the folder, it notified me that it was going to upgrade the database (which shouldn't be the case, as everything was already at 3.1.2), opened Keynote, and then hung.
AND THEN...I quit OpenLP, deleted the copy of my openlp data folder, put the original back (that was working properly), and opened OpenLP...and it hung.
So, there seems to be something about my database that not only causes OpenLP to hang (unless started via command line) and makes the defect permanent in that user account.