Seeing M cry makes me think about crying as akin to an audio feedback loop. In other words, like the ear-piercing squeal you get on an open microphone that is too close to a speaker: a single resonant frequency gradually gets picked up more by the microphone and in turn broadcast by the speaker more, leading to that tone escalating in volume until it's unbearable.
On this account, M has some overall level of arousal that she is trying to regulate (in the analogy, the sound signal being processed by the system). Some arousal is generated internally, e.g. gas, hunger, etc., while other arousal is external, e.g. seeing faces, bright lights, noise, us moving her or her limbs. Typically she damps down both internal and external inputs after they are processed in order to maintain her state. Noise makes M startle but she usually returns to sleep or equilibrium; gas makes her frown and squirm but once it passes she calms down. This is like a standard microphone system - put in sound and it gets amplified, then it dies away.
But at some points, M can't damp her inputs effectively, and you can see her face and posture change as the arousal builds up to a cry or a scream. The build up doesn't take that long, but I think every parent gets to be familiar with the signs: the wriggle, the scrunched up face, the silent mouth opening. What's interesting about this build though, is that (at least with M) it's been pretty easy to short circuit. Sometimes it's enough to change her position from lying down to sitting up; sometimes I can just say a word or two to her or bounce her a little in my arms.
If she has already started crying, though, it takes quite a bit more stimulation to get her attention. Thankfully, a change of position, eye-contact, bouncing, and a few words (maybe spoken a bit louder) will usually cut through, at least temporarily. In an audio feedback system, when you have some kind of amplification, putting noise into the system can override the feedback loop and reset the system. The more feedback there is in the system, the louder the external input needs to be.
Back to HBB. From the feedback loop perspective, 3 of the 5 Ss are ways of changing the dynamics of the baby's perceptual and input noise. Swaddling cuts down movement related stimulation; shushing is like injecting white noise directly into the auditory system; and swinging provides a lot of visual and vestibular inputs. The fourth, sucking, may be a bit different but it certainly activates a number of reflexive behaviors, which could refocus some of her internal processes. (I don't have a good account for why being in a side position matters - but this is also the one that seems to matter least for M.)
Although there's a tremendous amount of work on crying - especially focusing on how to reduce it - I haven't been able to find anything that I can really compare to this perspective. There are some hints about this general set of ideas in a classic 1962 paper by Brazelton, but the only quantitative work that I know of on this is a paper by Thomas and Martin (1976) on dynamic feedback loops between mothers and infants. Does anyone know about other relevant references on infant homeostasis, fussiness, or crying? It seems like this feedback loop framework makes many testable predictions...