What was the intellectual background before our first śāstras?

Do the similarities in the treatment of paribhāṣās (metarules) in Śrautasūtra, Mīmāṃsā and Grammar lead to the conclusion that Grammar, Śrautasūtra and Mīmāṃsā share a common prehistory or is the one indebted to the other? Dominik Wujastyk, in the Introduction to his edition of Vyāḍi's Paribhāṣāvṛtti, implicitly suggests a common prehistory, with possibly the Mīmāṃsā preceding Grammar in the usage of paribhāṣās:

It is a moot point whether or not Pāṇini actually had some of these paribhāṣās in mind as he composed his grammar; probably he did have at least some of them in mind, whether explicitly or not. A study of the earliest \emph{mīmāṃsā} from this point of view might throw some light on this question (Wujastyk 1993, p. xii).

In his PhD thesis, Sharon Ben-Dor, quoting Vashishtha Jhā, suggests that the direction of borrowing is from Mīmāṃsā to Grammar. All these authors leave the Śrautasūtras out of the picture:

Actually, the Pūrvamīmāṃsā can be viewed as the discipline that established this method. According to Jha, this discipline is a system that deals with principles (nyāyas) of textual interpretation for texts whose authors were no longer present. He adds that these principles were used by all the Indian philosophical systems, and argues that all the systems are indebted to Pūrvamīmāṃsā because it has provided the tools to interpret a text (Jha 1992: 2). [\dots] In respect to Kātyāyana, some scholars have indicated the close relationship between the vārttikas in the Mahābhāṣya and the Mīmāṃsāsūtra of Jaimini, and it is likely that some of the interpretive principles mentioned by Kātyāyana are adopted from this discipline. […] [W]hat is evident is that already in the time of Kātyāyana, this method of referring to daily life activities for interpreting a text was an established and accepted practice among Indian scholars (Ben-Dor 2009, pp.8--9).

This last element does, in fact, incline one to think that it might have been possible for Mīmāṃsā to influence Grammar rather than the other way round. For it is Mīmāṃsakas who trust ordinary experience, whereas Pāṇini tends to build a consistent system which only refers to ordinary linguistic use and it is not clear why other ordinary usages could bear any influence on the Aṣṭādhyāyī.

On paribhāṣās, see this post, which displays also further links on a possible common prehistory.