A Single T1 should be horribly easy to max out for a school, that doesn't sound like enough at all. 1.5mbps is hardly a high speed connection, even with a dedicated line, when you are dealing with a whole school. Where are you finding the actual lag to be coming from? All hops, or only certain hops?
I see, sorry, misread the 3 AM part, thought you said it was fine then. I would run a normal trace route, just to be sure the program isn't throwing you off. Seems odd that all the hops would be slow, even after the ISP. Cause even if the ISP was slow, it should still speed up after it passes through them and onto other networks. When you ran a sniffer, were you getting lots of packet drops or anything? Are you letting routing protocol broadcasts accidentally go through the WAN? Is your local LAN running fast?
Well, if you are losing packets that often after it leaves your gateway, it sounds like an ISP problem. I know an ISP will be hard pressed to take responsibility for any problems, even if it is their problem. I would call and complain again, tell them that you can trace, and anything past the gateway is having loss problems, as this seems more likely to be their issue, not yours. If I had to, I would record multiple different sites, and show them proof that it happens every time after the gate. They know they can just blame your network, and most people go away, I would keep with them, cause I just can't see anything else being the problem.
I honestly don't know of a program to do this, since ISPs really don't like you sniffing their traffic, or doing anything that would involve getting information back from their portion of the network.