Here's one for your "kitchen sink" file (a research study that throws almost every imaginable technique at a problem--and succeeds) . . . well, sort of. In Kinoshita (2015) over the course of a four-week course, students were taught using seven different, relatively standard procedures for working on Japanese rhythm with JSL students. If you are new to rhythm work, check it out.
Those included: rhythmic marking (mark rhythm groups with a pencil and then trace them with their fingers), clapping (hands), pattern grouping (identify type of rhythm pattern for know vocabulary), metronome haiku (listening to and reading haiku to a metronome), auditory beat (reading grouped text out loud), acoustic analysis (using Praat), shadowing (attempting to read or speak along with an audio recording or live person). Impressive! They worked with each one for over an hour.
Not surprisingly, their rhythm improved. It is not entirely clear what else may have contributed to that effect, including other instruction and out of class experience, since there was no control group, but the students liked the work and identified their favorite procedure, which apparently aligned with their self-identified cognitive/learning style. Although after having done that many hours of rhythm work it had to be a bit difficult for the learner to assess which technique they "liked" best, let alone which actually worked best for them individually.
Of particular interest here are the first two techniques, marking rhythm and tracing along with a finger, and clapping hands--both of which are identified as "kinaesthetic" by Kinoshita. (The other techniques are noted as combinations of auditory and visual.) They are, indeed, movement-and touch-based. The first at least involves moving a finger along a line. The second, clapping hands, could, in principle, involve more of the body then just the hands, but it also might not, of course.
Neither technique, at least on the face of it, meets our basic "haptic" threshold--involving more full-body engagement and distinctly anchoring stressed vowels. By that I mean that including touch in the process does not, in principle, help to anchor (better remember) the internal structure of the targeted rhythm groups--in fact it may serve to help cancel out memory for different levels of stress, length and volume of adjacent syllables. (There have been several blogposts dealing with this topic, one recently and the first, back in 2012 that focused on how haptic "events" are encoded or remembered.)
In essence, the haptic "brain" area(s) are not all that good at remembering different levels of pressure applied to the same point on the body. In other words, it is more challenging, for example, to remember which syllable in a clapped or traced rhythm group was prominent. (The number of syllables involved may be another matter.) So, to the extent that rhythm cannot or should not be divorced from word and phrasal stress, Kinoshita's two procedures probably are not contributing much variance to the final "progress" demonstrated.
That is not to say that more holistic,"full body" techniques such as "jazz chants", poetry, songs or dance, such as those promoted by Chan in her paper in the same conference proceedings (Pronunciation Workout), are not useful, fun, engaging, motivating and serve functions other than acquisition of the rhythm of an L2.
A basic assumption of haptic work is that systematic body engagement, involving the whole person, especially from the neck down, is essential to efficient instruction and learning. (Train the body first! - Lessac). v4.0 will include extensive use of "pedagogical dance steps" and practicing of most pedagogical movement patterns (gesture plus touch) to rhythmic percussion loops.
As always, if you are looking for a near perfect "haptic" procedure for teaching English rhythm, where differentiated movement and touch contribute substantially to the process, I'd, of course, recommend begiining with the AHEPS v3.0 Butterfly technique-at least as a replacement for hand clapping. And for most of the other eight as well as matter of fact!
Kinoshita, N.(2015). Learner preference and the learning of Japanese rhythm. In J. Levis, R. Mohammed, M. Qian; Z. Zhou (Eds). Proceedings of the 6th Pronunciation in Second Language Learning and Teaching Conference (ISSN 2389566), Santa Barbara, CA (pp.49-62). Ames, IA: Iowa State University.