Try Endeavor then. Still rolling release, based on Arch, but with some additional tweaks. Less tweaks than Manjaro, so it tends to have less drama, and a good arch derivative.
Right, that makes sense if you can't adjust your router's DNS. However, you can manually change the IP address of the DNS servers you want to use per device. I recommend trying to change the DNS on your computer or something to your pi-hole's IP address. If you do that and can get internet access you should be good. If not then you can check the pi-hole logs to see if it's getting any of the DNS queries. Feel free to DM me for more help.
If you set the dns address manually for a device instead of relying on DHCP does dns work then? That should work fine no matter what your router is giving out.
This might be a good option for you: https://elfhosted.com/