I have two old knife holes in me already and have met my quota of stitches. But I have learned some things along the way. My first priority in a knife assault would be getting my two hands on their one knife hand/arm and grounding that point somewhere. Everything else can be dealt with after that.
Break the knife if you can, or at least kick/throw it away. You want it out of the picture, asap. Because if the tables turn it can come back to haunt you. Until it's out of action, you can't use chokes or anything that's not immobilizing the knife and going for debilitating damage. IMO.
I agree your priority is to gain control of the knife. However, I think the dynamics of training require you to break this down into a smaller subset of problems that need to be solved. Gaining control of the knife requires that you have control of yourself and your opponent in some way. In my experiences, you need to disrupt the attack and then work to gain control of the knife.
There are a number of things in this dynamic from you pre-emptively entering to off balance and disrupt, to you in a very bad postion and then disrupting, orienting on the knife, and gaining control of it.
I think this portion of training is left out way too often and we just "let it go" and say "priority is to gain control of the knife"...and only practice that phase.
Not sure I'd spend much time on breaking a knife...not sure how you'd do that, your not gonna break my Cold Steel. Also even if you did, it is still a weapon and can inflict damage. I'd rather focus on the control.
I would simply ask you to consider about the small details you need to do that lead to control of the knife...that is all I am really saying. Again, I agree, getting it out of the picture as fast as possible is paramount.
Agree also, I am not too worried about chokes or other restraints until the knife is under control an in my possession.