Well played!

Although it might be worth mentioning here that you can script out login creation statements (with SID and password hash) to move logins from one server to another, which will work with databases restored from the same server. That's kind of what I thought this might be, when I first read the title. Microsoft offers this (https://support.microsoft.com/en-us/kb/246133) but their script can definitely be improved upon... although I don't think I've seen a good one posted anywhere? (I've seen a nice Powershell version, but not T-SQL.) Would there be any interest in that sort of thing?