They haven't "disabled all ping/traceroute related testing within the cmd prompt" unless it's a school pc. They are probably just blocking ICMP. UNIX traceroute defaults to UDP and you can set it to use TCP if that doesn't work. If you've only got Windows there's programs that can do the same (e.g. pingplotter).
You won't be able to fix the problem if you don't know where it is and can't even prove it exists at all. Point your finger at them all you want, but do you really think without any evidence this is going to help? They won't go "Oh well, I guess our network is fucked, we should definitely do something about this", they'll go "Ok, it's only a single student complaining and we can't reproduce the problem. Chances the problem isn't our network, instead his pc or the gameserver: >99%. Case closed."
In fact they pretty much said that.
The fact that you have any lag issues in the morning is a red flag to me that the problem exists outside of our network. In addition to that, we've received no complaints from other gamers who have similar low latency requirements. If this happens on all of the servers you connect to, the biggest issue could just be how the application is written to use the network. At this time, there is nothing we can do to improve the experience.
Right now to them you're just looking like a clueless student playing on a shitty gameserver crying that the internet is broken and they must fix it.
Sorry if this is all a bit harsh. My points are:
-Blaming people without proof is never a good idea.
-Just guessing what the problem is and then only trying to fix that even though there's a lot of other options what the problem could be, because "surely this must be problem" is never a good idea.
->Find what's causing the problem first.