Tom,
Part of what you may be experiencing is mid-route congestion, or it can be services queuing on the remote cluster end.
One thing that you can do from your end is to run a graphical tool like ping-plotter and see both current/average latency, hop count, and often device names. This will give you hints about where the traffic flowing and congestion points.
There are other tools that are more precise, and allow you to look at route tables/route resolutions, but they are definitely more 'deep-in-the-tall-grass' exercises.
