Here's a drawing of what I think might be happening to your private traffic: traffic diagram
One major benefit to this approach is CloudFlare does not need to revoke an entire public certificate authority (CA) if a singular private tunnel's Certificate Authority is compromised.
I have a similar issue when I am visiting my parents. Despite having 30 mbps upload at my home, I cannot get anywhere near that when trying to access things from my parents house. Not just Plex either, I host a number of services. I've tested their wifi and download, and everything seems fine. I can also stream my Plex just fine from my friends places. I've chalked it up to poor (or throttled) peering between my parents ISP and my ISP. I've been meaning to test it through a VPN next time I go home.