In a singing context, at least some voice training methods look to develop the ability to tilt the thyroid cartilage and (separately) the cricoid cartilage, as a way of changing tone and projection. For example, the Estill method teaches that the thyroid can be tilted forward by imagining you're about to make a whimpering sound.
On the other hand, Esling et al's Laryngeal Articulator Model does not seem to feature these movements. Unless I am missing something, the basic idea is that the larynx concertinas when raising of the thyroid combines with retraction of the tongue root and narrowing of the pharynx.
Does this mean that Esling et al. don't accept that the cartilages can be tilted (I'm fairly sure I can tilt the thyroid) or is the tilt subsumed in some other part of their model? I suppose there could be some other reason for leaving it out, but their overall approach does seem to be pretty comprehensive.