This has happened a few times before, actually. Dogfooding is good, but not for status pages!
Cloudflare does it right for their status page (https://www.cloudflarestatus.com). They don't use Cloudflare itself for it (you can tell because /cdn-cgi/trace returns nothing), the actual backend is Atlassian Statuspage, their TLS certificate is issued by Let's Encrypt instead of Cloudflare itself, and it's on a completely separate domain for DNS purposes.
Cloudflare does it right for their status page (https://www.cloudflarestatus.com). They don't use Cloudflare itself for it (you can tell because /cdn-cgi/trace returns nothing), the actual backend is Atlassian Statuspage, their TLS certificate is issued by Let's Encrypt instead of Cloudflare itself, and it's on a completely separate domain for DNS purposes.