Hi, I also run to work most mornings and find that it raises my bg levels by around 2-3mmols. I'm keen on sport and did a bit of research as I find different sports affect my levels in different ways (swimming lowers levels, climbing raises them). It seems the more high intensity the activity the more likely the liver is to be stimulated to release glucose. therefore when I walk the same distance to work my bg drop 2-3 mmols as it's lower intensity. I think you're right and that dawn phenomenon does play a part in it as well as involves the same adrenal hormones that cause the liver to produce glucose when running. I guess combined they make levels rise more perhaps?
The only way I've found to deal with it is to run to work, by which time my levels are often 7-9 and then take an extra half unit of insulin when I eat breakfast at work. Within an hour they're back to normal. Look on the Runsweet forums, there are quite a few discussions about running and high bg levels. There seem to be some suggestion of keeping a steady pace would not increase levels so much.
Everyone's different so I guess you just have to find the routine that works for you, good luck with the running!
Fran