As a follow-up, this guide: Troubleshooting SSL/TLS issues helped diagnose the problem a bit further, it appears my computer is using the correct Cloudflare IP for the site, but my browser is still using the old site IP.
After trying it on a new computer, the new issue seems to be that About Seacoast Properties | Seacoast Properties | Seacoast Properties | Seacoast Properties | Seacoast Properties is causing a redirect loop in which the origin server is redirecting HTTPS traffic to HTTP and Cloudflare is doing the opposite. This article seems to indicate that the “flexible” configuration is not compatible with a redirect from HTTP to HTTPS, but is the reverse the same (the origin server redirects HTTPS traffic to HTTP).
This seems odd to me as my understanding is that Cloudflare communicates with the origin server over HTTP when “flexible” mode is on, so the server should not be sending a redirect from HTTPS to HTTP.