Convert Existing WP Multisite to 100% HTTPS/SSL Secure

I have read through tons of postings, here, on WordPress.org, and elsewhere. While there are lots of problem-specific fixes, I am yet to find a guide to converting an existing, working WP Multisite to HTTPS/SSL. While it would have been better to start from the beginning embracing HTTPS, my case is an existing site. In a "normal" WordPress installation, it is a matter of just changing http to https in one spot and then hunting down the "hard coded" http references, either manually or with a plugin. Multisite is a totally different beast.

Do I have to unload/backup the exiting multisite and start from ground zero with a clean multisite installation and reload the backups, taking care of references in the database tables?

I am looking for a guide or guidance. I appreciate any help available. I would be happy to write that guide as a result of this journey to SSL too!

Thanks in advance (and apologies if I missed something here or elsewhere).

Jim

Environment: Current WP release with all plugins up-to-date. Multisite using sub-directories. SSL certificate purchased, installed, and working. Apache/CentOS/WHM/cPanel platform.