Private memberships / invite-only is already a feature - you can toggle “Allow free member signups” to disable signups.
However, @sjmscott it seems like a huge workaround to what is probably a configuration problem. If you share more details of your original problem we can likely help you get it resolved.
Thanks, Hannah. I figured out one of the links was taking users to a welcome page that didn’t exist. I have created the missing page and I think I’m good.