It seems to me the correct approach is to block DNS to all servers but the ones you want to allow in the Access Policy.
The one(s) allowed would be provided by DHCP.
Destination NAT must be a 1 to 1 mapping (i.e. you cannot map multiple destinations to a single one using a single rule).
If you have clients that MUST use a specific DNS server that's not a preferred one, you could create a specific NAT rule that routes the request to your preferred destination.
Something like:
Original Source: Client IP range
Original Destination: 8.8.8.8
Original Service: DNS
Translated Source: Gateway (Hide)
Translated Destination: x.y.z.w
Translated Service: Original