Follow up, for me, this is looking like an 70% GoDaddy, 30% Cloudflare issue.
First, the IP issue solved site 1. Not sure how a site can have multiple IPs on a GoDaddy server but hey, worth checking out if you’ve moved, restaged, something one of the sites.
Second, on site 2, turning on WP debugging revealed a number, 3-5, of PHP/WordPress deprecation warnings. Again, warnings not errors. (And not PHP warnings but WordPress function deprecated warnings.) What’s more, these only showed in the admin. That said, I patched the older plugin, and turned off SSL and the site is back up. (Cloudflare SSL is giving me errors for the moment.)
The errors from the plugin occasionally stopped WordPress from fully loading the administration which is what tripped up Cloudflare. What doesn’t make sense is, I could not get these errors/warnings to show on the frontend and, without explicit errors on, these didn’t even show before at all, anywhere. My guess is an error was in one of the headers sent from GoDaddy to Cloudflare and Cloudflare read this as the site is down, not just errored.
GoDaddy is mishandling PHP Warnings, Cloudflare is considering 1 error header as the page is “down.” Hopefully that helps someone.