My setup is different from yours, but maybe it’ll be a reference for something you could do.

I use WireGuard. I forward my dns over the tunnel. The dns servers are my home dns servers (pihole). Those servers resolve my host Ames to their LAN addresses. Those LAN addresses are reputable when I’m connected with WireGuard. This means I use the same IP addresses and same host Ames over vpn or locally on the LAN.