Remember the old "thundering herd" problem with Apache children and things of that nature? You'd basically have a whole bunch of processes which had a listening fd from an earlier call to listen(). When a new connection would come in, the kernel would wake all of them, even though only one of them would actually have something to get. The others would go through the process for nothing. It caused a big performance hit back in the day.
Well, imagine now that you have a directory or lock service where you can store things and perform atomic updates. When you do a write to something in it, it fans out to all of its clients, and they all wake up (nearly) simultaneously and receive the update. They then have to do whatever processing you do with new data of that type.
If they all do this at the same time, then you have no processes left to service incoming requests. They're all identically busy with whatever mutexes held in order to apply those config changes safely, so no other work happens on those clients while they load in the new data.
It's not so much that it's taking a mutex and is getting stuck for a little bit, since that's going to happen no matter what. It's that all of the children do it at the same time, so there's nobody to service your hit, and you're guaranteed to get stuck. If it was spread out, then only some percentage of incoming requests would get stuck behind this. The others would get lucky and would hit another instance which either had already run it or hadn't yet run it.
I'm not saying this is what's going on here, but it sure sounds familiar.