Keeping the hair trimmed is a good idea. You could try rubbing cornstarch in the hair and then try combing it out it not too matted.
What breed of dog is she? Does she have long hair around her mouth? If so, you can have a groomer (or you can do it yourself if you have clippers) give the hair around her mouth a close shave, so to speak, to remove the hair that the food and dirt cling to. Eliminating the hair should eliminate the problem. I tend to agree with you that it's a combination of saliva, dirt and food build-up, and it's pretty common in dogs with "beards".
Ghilly