The following is admittedly, at best, perhaps only obliquely related to EBTs…
In Chinese Buddhist writings on breath meditation, far more prominent than the soḷasavatthuka, the sixteen steps of ānāpānasati, are the 六妙門, “the six sublime gates,” or the 六事, “the six matters,” which encompass six (數, 隨, 止, 觀, 還, 淨) of the eight steps (gaṇanā, anubandhanā, phusanā, ṭhapanā, sallakkhaṇā, vivaṭṭanā, parisuddhi, and paṭipassanā) of the Theravādin Visuddhimagga tradition (i.e., nos. 1-2, 4-7).
(It should be mentioned that the 解脫道論/Vimuttimagga [also a Theravādin tradition(?)] features four of the eight: 算, 隨逐, 安置, 隨觀, or nos. 1-2, 4-5.)
Does anyone know of any contemporary teachers actively teaching according to these (again, admittedly somewhat later) formats?
For the general audience: Rightly a complicated matter. Dhammapala attributes this to Abhayagiri Monastery, which was Theravadin by Vinaya standards, but with a few twist on some ideas. For example, Vmt and Vsm disagree substantially on certain topics.
Ven Analayo notes this as a source:
Dhammadīpa, Bhikkhu 2009: “Two Divisions of Ānāpāna-sati/smṛti in their Chronological Development,” in Buddhist and Pāli Studies in Honour of the Venerable Professor Kak-kapalliye Anuruddha, K. L. Dhammajoti and Y. Karunadasa (ed.), 567–582, Hong Kong: University of Hong Kong.
Pa-Auk Sayadaw’s lineage is the living transmission of the Visuddhimagga format, though I don’t know of the details.
As for the Chinese Six Gates:
Jiryu Rutschman-Byler, a Soto-Zen priest teaches the six gates though the source I’ve found asks not to be distributed. Though you can find his writings trivially I assume.