Correct, newreview is specific to the second chance pool. I think it’s the main way that stories are found for it — a reviewer digs through newreview, and when enough reviewers agree a story is good, it’s accepted into the pool. That’s not the only way (you mention another), just the main way.
If you’re interested, I encourage you to email and ask if you can join. They’ve probably long filled the team that does it, but it’s always worth asking if you want to do some yeoman work. But one tip: it’s work, not fun, so if you do pursue it, be sure to go into it with that mindset.
To be honest, I doubt they need any help nowadays. The system has been working well for nearly a decade. But you never know till you try.
I've recommended items to that myself (from other people), via email to mods. Those are usually accepted, though not always.