I am certainly no expert but when reading your post I was reminded of a problem I have had intermittently in the past and one that I still watch out for. I had the habit of involuntarily closing my throat for a second or two while playing and unlike you I was not aware of it until pointed out in a lesson I took from a fellow band member. I am wondering if the movement in your throat is the involuntary closing that I experienced?
Greg’s concept of the “body’s concert hall” with door, foyer etc may be helpful for you to focus on along with the ” MM-AHH-OOO”. Before practicing, I now do this little exercise regularly along with beginning full breath (with the knuckle in an open mouth) to remind myself to keep the throat open; I feel it has been helping.
Further to this comment, I would also advise you to stick with the process Greg outlines despite occasional setbacks or slow progress. I am a little further along the course than you and feel it is slowly helping me despite a number of bumps along the way. Still a work on progress but there is progress.
I hope this may be helpful to you. Good luck with course.