As you said pros and cons to each. In addition to what you said.
Opening it up to new registrations
-If there were designated hours it might get people to show up for those times as it's hard to connect with people if there is a low chance they will be on when its on all hours.
-Moderated chats make people feel safer.
For it being not open to new registrations
-Being able to chat 24/7 is nice
-Using it as a pm system like you said is nice.
The issue is I don't know enough right now. I mean how many mods do we even have? There's about 5 people that even chat on Girl Chat right now period. So how many times a week will it be open?
I honestly think the bigger deal right now would be getting registrations open on the main site.