I'm open to being granted a special dispensation to browse and review the queues that I'm "not qualified for" because of "low reputation". I'm sure that a fair number of others that are equally qualified to look at close votes but are disqualified due to reputation would be willing to assist in helping to process the queue.
Maybe some formula involving [time on site] and [reputation] could come to some reasonable but lower threshold for users that "are probably qualified" to look at close votes.
It's apparent that whatever the criteria is now (reputation entirely) is not a good benchmark for this task. If the buffer is continuously overrun, then it means you don't have enough processors processing.
I'm willing to be a processor. Let me have at.
[edit]
More specifically, "Is this simply caused by the lack of reviewers or ...?"
Yes. For the quantity of input, there exists a shortage of processors for said input. The solutions are simple. More processors or less input. Less input seems to not be an option since input is a public-facing device. This obviously means that more processors are necessary. Tempting or taunting current processors with even more stuff to do, does not a solution make. You need more processors, an entire pool of unused ones is available. Put them to use. Make each vote only count for half a vote if that is what is necessary to mitigate the unqualified that make the cutoff. The current state of things points to things getting worse before getting better.