We had to edit /etc/init.d/wireguard to use the DNS entry on the Slate Wireguard Client configuration page. This edit modifies the dnsmasq DHCP configuration to deliver the configured DNS server when the Wireguard VPN comes up. Unfortunately this fix requires the computer clients to renew their lease after the VPN is established to retrieve the new DNS entry. Without these changes, we were unable to make the Slate clients direct their DNS queries to the configured DNS server through the tunnel.
We also modified /etc/config/dhcp to deliver local search domains. This fix is less than ideal because it can not be configured for each VPN server attached to. It is persistent between VPNs.
Hopefully this will help someone else using the Slate router with Wireguard.
Here is a link to my blog that describes the fix.
I would have posted the information here but I got an error about “new users only permitted two links” or something like that.