I think having a cooldown on a limit per account for referrals would combat this. For example - You could refer up to 5 email address with sign up requests and then have a cooldown of so many hours or days before being able to again.
Not really sure about how that could work fully as the thought just came to mind - But thinking a lot about what you said regarding people being able to take advantage of it - This could work. But yeah - Something aesthetic but non impacting stat wise or item wise would be a nice reward for friend referrals.