Being a somewhat lazy sort, I would plan on a bit of cutting in an up/down motion through the mat (like Stevenson's suggestion), not across. Since he is obviously not a show horse this might be a bit of a time saver for you. Show Sheen makes for very slick hair and the blue Oster mane and tail brush is my favorite grooming tool (as per someone else's suggestion).
But if you have the time and he has the patience go for the other suggested methods. Post a photo of the finished product! : )
If you ever find yourself in a fair fight, it's because your tactics suck. ~ Marine 1SGT J. Reifinger