The “solution” mostly lies in the fact that I got lucky. The parameters of the project changed so that it’s not a moderated system anymore. I’m now using the “Invite Anyone” plugin to allow users to invite friends. There’s an option there that allows account activation via invites even if registration is disabled.
Not as good as allowing anyone to register and moderating those requests, but seems to be the best compromise until this plugin gets rewritten for the newest versions of WP & BP.