Is there anyway to have specific service's notifcation superscede that of another one?
AFAIK this is not possible (at the moment). Perhaps because it is difficult to implement.
Even though, say, HTTP service goes down at the same time as ping, to The Dude this may not be the case. The Dude does not probe everything simultaneously. So it might not be apparent to The Dude that everything went down at the same time. So then you'd have to introduce some kind of time frame in which The Dude may assume everything went down at the same time, even though this is not what is probed. This delay in itself may cause problems, because you may not be informed as soon as possible. Etc.
One could perhaps argue: too little gained for too much development effort...
And still: it's possible that while ping is down on a server, other services aren't...