Invite only exclusive vs free sign up

I'm working on an app in a crowded space (property management) and trying to decide how to gain traction. Currently the app is free to download and use. I'm planning to do a marketing campaign next week. I could do the campaign around signing up for access to an invite only app (like Superhuman), or I could keep it open and free to download. I'm leaning toward invite only. It seems like people really get excited about the exclusivity (as Clubhouse has done). Hopefully this discuss could help with others facing the same decision.

My app is called Allen if context helps for picking a strategy.