Have you tried with DNSCrypt proxy instead of Cloudflared proxy? I have been having very good luck with the DNSScrypt proxy on many Pi-hole installs as both stand alone Pi-hole's and docker based Pi-hole's. I have the upstream DoH servers being both Cloudfare and Quad 9. In my toml file it was very easy to setup only had to update two lines one for the server and the other was bind to the network and port.
server_names = ['cloudflare','quad9-doh-ip4-port443-nofilter-pri']
listen_addresses = ['127.0.0.1:5353', '[::1]:5353']