I can’t change my router’s DNS
Do you mean you can’t change the DNS server in the DHCP settings or the server the router itself uses? In the first case you might be able to use Pi-Hole’s DHCP server instead, while for the latter it shouldn’t be an issue - I actually usually leave upstream servers configured there to avoid loops. BTW, you might also be able to flash OpenWRT to your router
You might be interested in CyclOSM to plan your routes