After putting in some better error output into the running scripts & functions: update-core.php and class-wp-upgrader.php I tracked it down to a permissions issue w/the following directories and files:
* wp-admin
* wp-includes
* wp-login.php
* readme.html
By default, we typically have our wp-includes directory writeable and our other directories locked down. To successfully run this upgrade, you must first make the previous directories & files writeable by apache user and then lock it down after you upgrade.
As for changing permissions via FTP – this looks like a decent step-by-step: https://www.networksolutions.com/support/how-to-change-file-or-directory-permissions-via-ftp/
