On Vyāsa and the authorship of the Saṅkarṣakāṇḍa UPDATED

(apologies in advance for the partial lack of diacritics, I am home, ill, with no access to a unicode keyboard)

The Saṅkarṣakāṇḍa (henceforth SK, about which see here) is an enigmatic text thought to complete the Mīmāṃsā Śāstra, after the Pūrva Mīmāṃsā Sūtra (henceforth PMS) and before the Uttara Mīmāṃsā Sūtra (or Vedānta Sūtra, henceforth UMS).

As for its origin, several witnesses speak of the SK as having been authored by Jaimini

How many texts are comprised in the Mimamsa Sastra? And why is it relevant?

(apologies in advance for the lack of diacritics, I am home, ill, with no access to a unicode keyboard)

Purva Mimamsa authors are generally not interested in the topic, whereas several Uttara Mimamsa (i.e. Vedanta) ones deal at length with the status of the Mimamsasastra (I am tempted to say that, similarly, Christians alone are concerned with the unity of the two testaments within the Bible).
A particularly puzzling element, in this connection, is the status of an “intermediate part” of the Mimamsasastra,