I do not have any medical credentials. I am going to suggest that it would be highly unlikely that your larynx is moving up while slurring as in swallowing. What you may be experiencing are movements associated with the hyoid bone. Movement of the jaw and tongue can move the hyoid bone upward and relaxing the muscles associated will allow the hyoid to be pulled back into a relaxed position.
Swallowing does involve the hyoid bone and more. When swallowing, the larynx is pulled upward and the epiglottis, a flap of cartilage, bends backward to close over the larynx’s opening that leads to the trachea and down into the lungs.
I have read that singers practice lifting the larynx by starting to swallow and not going through with it. If there are any singers out there, maybe they could explain this.
Now for an experiment. Place your fingertips on your adam’s apple and swallow. Does this feel like what you experience while doing the lip slurs? Hopefully, you do not. Now place your fingers above your adam’s apple. Simulate lip slurs without your horn and with your horn. Do you feel the contractions of your muscles or perhaps the motion of your hyoid bone? Because the hyoid bone is connected with your larynx you may feel some motion there as well, but it is not like swallowing. Check this by placing your fingertips on the larynx. These are the natural motions associated with changes in the tongue and jaw.
Now the question we need to ask Greg is how much jaw and tongue motion is involved in doing these slurs? Should we try to focus more on changes in lip contraction and minimize other motions?