Perhaps you could configure more than unbound service behind a loadbalancer. Each unbound instance is configured to use different upstream dns servers.
Double check if unbound doesn't allow you to randomly hop between dns upstreams first, but the above solution should work if that's unavailable atm.
Not sure you would even need encryption. Surely It can't be illegal to ask the root servers (and all the other DNS servers involved, because the root servers only have IPs for TLD DNS servers) for IPs