Hi Matt,
I'll get to your points to a second. First up though, this kind of detail would have probably got some more interesting results for you if you had of put it in the original question.
Moving on, it sounds to me like you are going to have to do some research into what is happening on your network. For example the obvious one is emails. If you are sending a large email to the site, they will be consuming a fair portion of the bandwidth. I would expect to see bigger latencies during this time. The only real way to control this is to introduce QoS (Quality of Service) on your network.
I also want to clarify, how are they connected back to your head office? Are you a hub and spoke network with the head office at the centre or is the head office just another spoke with a large teclo acting as the Hub for internet access and the like. If the head office is the hub then you may have contention on that link that is causing it to flood. You are going to have to share more details and do some work on the infrastructure side to document and understand what is happening and where.
I know from experience, we spent a lot of time trying to track down timeouts in specific sites (I work for a large retailer), we found emails as being the primary cause in a lot of cases.
Hopefully that sheds some light for you, happy to continue this conversation.
Chris