One way you can get around this and still use 1.1.1.1 for most sites would be to use a local recursive resolver that supports domain name-based upstream overrides such as dnsmasq, and setting that as your local resolver.
You can run dnsmasq on anything that can run arbitrary services e.g. on your local workstation, or on your router if it is open enough, or even on something like Termux probably.