The more I've messed with it, the more I think that I just can't reach those domains for whatever reason.
The fact that I don't even get a confirmation on Clodflare's test site that I'm using their DNS, when I can verify that I am through other methods, makes me think this is some fringe case and DoT is actually working fine.
It's possible your ISP or County do not allow encrypted DNS over TLS via cloud flare domains since your encrypting the dns domain lookups. That's not to say they can't see the reverse lookup the ip address your connected to but likely more of a pain in the butt. That said I have no idea why you cannot connect to cloudflare via DoT. My suggestion would be to attempt to use a vpn on the router with DoT or a VPN on your computer with a browser with DoT support.