I completely fixed this issue plus the spinning wheels by:
1. Highlight All Notes, choose File: Export Notes... and creating a backup of the entire database.
2. Using the freeware AppCleaner (https://freemacsoft.net/appcleaner/), I completely deleted all files associated with Evernote.
3. Download a fresh copy of Evernote (I'm running Mac OS X 10.14.5), and Import the database file.
Did this a couple weeks ago, and no more spinning wheels and no more request to Keychain sign-in.