Does the commercial helicopter training in 61.129(c)(3)(i) require a CFII?
A CFI can give the training because it's training "solely by reference to instruments". If it were "instrument training", you would need a CFII.

See the Jablecki (2016) interpretation, which addresses your specific question:


  In order to provide instrument training for a commercial pilot
  certificate or ATP certificate, a flight instructor must have an
  instrument rating on his or her flight instructor certificate.
  However, §61.129(c)(3)(i), unlike its counterparts in §61.129,
  does not have a requirement for "instrument training" as defined in 14
  CFR §61.1. Instead, §61.129(c)(3)(i) requires training on the
  "control and maneuvering of a helicopter solely by reference to
  instruments." Therefore, the training in §61.129(c)(3)(i) is not
  considered "instrument training" that requires a certified flight
  instructor to have an instrument rating on his or her flight
  instructor certificate.