Why have a timer until matching attempt occurs at all? It would make sense like @Gibsaw already pointed out to try to match as soon as somebody new joins the queue for example. If nobody new joins and nobody leaves the queue the only thing changing is the duration the people are waiting, and even then it doesn't make sense (except from easier algorithm implementation standpoint) to have regular matching intervals, but rather it would make more sense to have some threshold values. For example, if people are more than 2 minutes in queue and gap between rating is somewhat big, but not too big, match.
You said:
"Having these regular cycles makes it easier to track how long people have been waiting in the queue than if we matched at irregular intervals."
Could you elaborate what do you mean by that? You could just have a timer that tracks how long you've been in the queue alredy, not a timer that tracks how long until matching attempt. That brings me to the 2nd point: Even if you keep the current matchmaking algorithm it would make more sense from user experience standpoint to only show duration you've alredy been in queue. Why expose one detail of how matchmaking works (by showing it only matches on fixed interval) if you don't expose any other details and the queuer still doesn't have a good way of tracking how long they've already been in the queue? Just my opinion of course.