There is no need to bring it down, close the port 53 on your server to the outside world and use a VPN to connect your computers to your root servers as @DanSchaper suggested.
Okay, thanks for the reply.
Maybe I'm wrong, but I think VPN is not an option because it's still a public server running my domain, right?
So I guess the best solution is just to buy another pi or put it on my synology.
The VPN secures communications from the clients to the servers. So you would have to have VPN software installed on all the clients and that creates a virtual private network between the clients and the server. The Pi-hole would be only connected to the VPN end point and not open to everyone as it is now. If you can install it locally though that would be the easiest solution.