Thanks everyone for the additional comments.
The 3.3 update was released while I was looking at the 3.2.2+ update, so I installed that version.
Please see summary at moodle before attempting.
My upgrade process reported that I met minimal requirements, but I found PHP 5.6 abhorrently slow. PHP 7.0 resolved this issue.
Process takes awhile, but here's what was successful using cpanel.
1. Full backup and database dump
2. Upload tar file to site root (or whichever folder /moodle directory resides)
3. Enable Maintenance Mode (Administration > Site administration > Server > Maintenance mode)
4. Rename current moodle directory
5. Expand tar file (cpanel file manager)
6. Copy config.php into new /moodle directory
7. If you have downloaded and installed non-core plugins, copy those to correct folder(s)
8. If you have downloaded and installed non-core themes, copy those to correct folder(s) as well.
9. Disable Maintenance Mode
10. Run Moodle update (Administration > Site administration > Notifications)
The update is thorough - it will advise if plugins are missing. It will not advise if theme files are missing until all missing plugins are found.
12. I reenabled Maintenance Mode at this point to review/test the site.
11. After update, I purged all caches. (Site Administration > Development > Purge all caches)
12. If your theme appears to be having issues, resave the theme settings (Administration > Site administration > Appearance > Themes > Theme settings). and navigate to the theme selector page (Administration > Site administration > Appearance > Themes > Theme selector). Theme should reload.
13. Disable Maintenance Mode