I have some advice. I'm getting used to it too, so not much.
First off: I highly recommend your group becoming a Moderated Group. It allows people to request access, so people who are interested in joining can request to.
Second: try making a small "government" for your group. TTC has an Elective Officer(Scribbler) who is basically the deputy, and both me and Scribbler are ambassadors, which are people who are up to date on the latest information for the group.
Lastly, you should probably use your description wisely, to say anything needed for people who want to join. Maybe that dupers aren't allowed, or that you're in an alliance with us, etc.
I think the ambassadors for each group should join the other group, so we can relay more information to our fellow members.
Even though people who do TTing/non TTing will probably join the right group, I believe both groups for accept members of the opposite. I have about 5 non TTers/former TTers in my group and we treat them like any other member. If we go "play style exclusive" then it may make people think we don't want members who are different from us, and it further divides us. I find the description of your group to feel a bit like that, because it says "if you don't time travel or dupe". With tensions high, it may stir up arguments. Like I said, it's just so TTers/non TTers will feel welcome in both groups, even if the groups are dedicated to one play style.
I'm sorry if I'm yammering on like Rover, I just would like our goal to be achieved as fully as possible.