Membership plugin to only show content published since registering

I’m looking for a way to restrict content displayed to subscribers based on when they registered.

Basically, every week new content will be posted and I want to be able to restrict subscribers from seeing old content and only seeing what’s published say a week before they registered and everything else going forward..

Is there anything out there that can serve this? I was thinking of using Ultimate Membership Pro to run the main bulk of the work, but this feature doesn’t appear to be available with it so I’m open to offers.

Thanks.