Mīmāṃsā and Vedānta: a historical problem

The relation between Mīmāṃsā (also called Pūrva Mīmāṃsā, that is Earlier M.) and Vedānta (also called Uttara Mīmāṃsā, that is Later M.) is more than controversial. Indian authors, both ancient and contemporary, all agree in linking the two currents of thought. But how is this relation to be understood?

1. 1. Did Uttara Mīmāṃsā evolve out of Pūrva Mīmāṃsā?
2. 2. Were PM and UM once the same school?
3. 3. Did PM and UM just become similar?

Pre-Halbfass scholars of Indian Philosophy usually assume something like n.1, and in fact Vedānta adopt the whole hermeneutic structure of PM.
Asko Parpola (WZKS 1981 and 1993) holds theory n.2, and maintains that the basic text of the Ur-Mīmāṃsā, the original "Mīmāṃsāsūtra" was composed of what became later known as the Mīmāṃsāsūtra and of what became later known as the Brahmasūtra. The names PM and UM refer, hence, to the first and the second part of a text (and not of an earlier and a later school).
Johannes Bronkhorst (see his Introduction to Mīmāṃsā and Vedānta: Interactions and Continuity) upholds n.3. In summary, he maintains that the Vedānta evolved in a very different milieu than the Brahmanic milieu of PM, namely the śramaṇic milieu of Jainas and Buddhists. Later, the Vedānta adopted the hermeneutic strategies of PM because they were prestigious and thus granted it acceptance and favour.
Against 2: Parpola's evidences are interesting, but far from being conclusive, especially insofar as he could not locate an early source talking of "PM" or "UM", not to speak of the absence of passages referring to a "pūrva-Mīmāṃsāsūtra" and to an "uttara-Mīmāṃsāsūtra".
Against 3: Why are so many Vedāntic authors (such as Bādārayaṇa) reverentially quoted in the earliest texts of the PM? This would not have been the case if the two originated in altogether different milieus. Could one maintain that Vedānta authors later used these names (and their texts?) to support positions which were completely new?
Do readers have an opinion about it?