When we get behind on replication, we tend to stack up background processes
behind a linearizer. Bg processes are heavy (particularly with respect to
prometheus metrics) and linearizers aren't terribly efficient once the queue
gets long either.

A better approach is to maintain a queue of requests to be processed, and
nominate a single process to work its way through the queue.

Fixes: #7444

... because stock `typing` doesn't have it in Python 3.5.