If you're expecting that there will be a way you can "get" some other volunteer to review your site more quickly, then your expectations are too high. The site suggestions are there to help the other volunteers find sites that fit their priorities, not to impose other priorities on them.
The "backlog" of sites to review is the whole internet. It's large enough for many more volunteers to explore. And anything in it is "fair game" for any volunteer to review.
The way to get a site reviewed is basically (1) make sure it's a compelling presentation of unique information about an interesting topic, then (2) make sure the editor can find it. You've taken care of part 2, by suggesting the site to a relevant category. (That is a help, it may not be all that much of a help, but it's all you can do to help, at least so far as that site goes.)
How about part 1? Unique information is easy, if you have it: just post it. Compelling presentation basically means "we can find it, and recognize it as unique" (in other words, we're easy but not omniscient).
How about "interesting?" That depends on the people who are volunteering today. And who knows what'll interest them today? That's the really random (that is, uncontrollable and unpredictable) part. The only common factor is that they're curious people, accustomed to look for authoritative answers.