Wireguard is simple enough to setup, and i actually use it much like OP does, though i don't force all my DNS queries through it, and instead use NextDNS.

It's basically setup so that i have my internal machines registered in NextDNS as rewrites, and Wireguard is setup to route anything for my internal RFC-1918 network, ie. 192.168.1.0/24, so when NextDNS returns 192.168.1.5 for "host.mydomain.com", it will go over wireguard.

The advantage is that i can keep the tunnel up 24/7, and it has very little impact on battery life as normal requests simply go over the internet.