OK .Yes you shouldn't remove Everyone from System policies unless you have another way of logging into Gatekeeper as an administrator. And it will be impossible to log back into Gatekeeper until you make a registry change. See
this post on how to do that.
Let's back up a little. As you found out System policies can have an adverse effect on the ability to control WG if they are modified incorrectly. I feel that you would be better suited to apply these policies in one of the other WG services such as ENS (NAT) or WWW proxy. How are your client computers connecting through WG to the internet - by NAT, direct proxy or Transparent Proxy?
Once you get back into GateKeeper you could add the group policy to the appropriate service and ignore the system policy for that service. This way Everyone can still connect to WG and utilise its' services but the sub group will be restricted in their browsing.