This is a Catch-22 situation where I could see issues either way:
If you don't follow-up, then you are someone that will say one thing and not do it. This would be a dangerous precedent. Thus, it may make sense to follow-up and see if there is an updated timeline for when you'd hear something.
If you do follow-up now, then there may be little for the company to tell you. Thus, they are going to say, "It's in process. We'll update you when we have something." While you may be seen as a pest, at least you did follow through.
If you wait 10 days and follow-up then, it may a way to split the difference between when you said you'd follow-up and the timing in the process overall at this point. This could be a useful compromise though it is a week and a half later than when you said you'd contact them so that blow could still apply. You could retort that because the deadline changed, you figured that you'd update when you would contact for a follow-up by that same time period.
At least those are the choices I see and how each may go poorly. If you do follow-up with them now, I'd be tempted to inquire if the process being delayed was a one time thing or if it is common for that to happen. While this may seem like a simple question, it may be useful to have the answer that delays are common and so after your interview you may have this again assuming you have an interview.