My thoughts may be a little different and I almost hesitated to say anything because I don't know your dog. And I may be underestimating the seriousness of your particular situation. So just take this for what it is worth... it may be worth nothing!
When Catcher was a young puppy, the first couple times I tried to take something out of his mouth he tried to bite and would also clamp his mouth closed so I couldn't open it. If I tried to groom him, he tried to bite and was like a snapping turtle... I even contacted my breeder about it. Catcher was purchased from a "professional" breeder, not pet store, broker, etc.
The way I decided to handle it was with love and letting him know I was alpha. I truly think he was doing this because he was just freaked out... like he was thinking "yikes, why is she opening up my mouth... help!" So, I was very, very gentle with him and spoke lovingly while grooming him and tried to make it fun and special. I also made sure he knew I was alpha. If I have to do something to him like examine an area on his body, I speak with him softly and and gently and he'll let me do it....
Now, I can open up his mouth any time and take Kleenex or whatever out of it and there is no problem at all. He is very good when I groom him. Last night as I was brushing, etc. I was thinking how far he has come. He'll even let me completely comb his moustache area which before he would not let me get near with a comb.
I think dogs act out sometimes when they feel threatened. I wonder if that is the case... he was scared of what you were going to do to him when you were messing with his coat so he was on the defensive.
IMPORTANT: You mentioned doing the alpha roll on him (putting him on his back, etc.) Do a Google search on the term "alpha roll" and you will see many articles that indicate that it is not in favor among dog trainers any more. Many years ago this was "the thing" to do but not now. I don't like it. Back in the early 90s I did it with my first Maltese Rosebud and besides not working, I truly think it negatively affected our relationship.
Again, this is just my experience and it may not be applicable to your situation with Gizmo.