Even if you do that, there’s some devices (Chromecast, Google Home) that have Google’s DNS hardcoded and ignores the servers passed by DHCP.
Something like...
iptables -t nat -A OUTPUT -p udp --dport 53 -j DNAT --to x.x.x.x:53
...should work, and repeat for tcp
[1]: https://mailarchive.ietf.org/arch/msg/dnsop/WCVv57IizUSjNb2R...