I feel the thing to do is to maybe have a vet check to make sure he isnt reacting this way for a health reason. It sounds unbelievable but there are people who have had deaf dogs and the dogs have been so clever they haven't realised

Now I'm not saying your Parker is deaf, but just using that as a sort of illustration to show that there can be health reasons for dog behaviour.
A behaviourist may be able to help or improve matters, but a lot does depend I feel, on why Parker does this. I suspect there is no health problem and he is fine. At the end of the day, I expect he is really sweet, but he is a terrier and maybe he just wants to hang on to his particular "resource" at the time.
I wasn't quite clear whether he snaps and bites just in the bed or at other times, presumably it is basically when he is comfy? If he is just bolshy then it is often possible to "re-train" the dog to understand he must listen to what you want :)
Lindsay