Hey Kyle!
You'll be surprised but miracles happen
.
After your yesterday request of admin login details, I was trying to figure out which is the best way to give you an access without any risk of data/site availability loss. Finally I decided to upload the site copy to a testing subdomain in order to make it separate form the main site. A new database with imported contents was a part of it too. After I've done this, I've double-checked if these user emails work on the subdomain - and they worked! (while on the main site they still did not). And the only difference between these 2 site copies was a database name and user.
And you know what? I've created one more clean database, imported the contents and switched the site to this new one - after that everything works fine with the emails!
So, even without knowing a reason, I've managed to solve the problem. And in fact you helped me a lot - if you wouldn't request a super admin access I wouldn't do all these moves.
So thanks very much! If you have any ideas about it - share with me please.