I do not know about the different practices in all oral traditions across India.
However, in my opinion your interpretation of the Sutra 1-2-31 समाहारः स्वरितः is not correct. The Sutra does not mean that Svarita has a pitch that lies between those of Udaatta and Anudaatta. समाहार does not mean "between", rather it means collection, assembly or combination. So the Sutra is better interpreted as "that which has the combined features of both Udaatta and Anudaatta is Svarita." How are these features combined in a Svarita? This is explained in the next Sutra 1-2-32 तस्यादित उदात्तमर्धह्रस्वम्. The Svarita has the features of the Udatta (high-pitch) for the initial half-instant and Anudaatta (low-pitch) for the remaining part. In other words, Svarita is a "falling pitch", and not "pitch between Udaatta and Anudaatta". Note that Panini does not mention the exact frequency/pitch in the Ashtadhyayi. He also does not say that the initial high-pitch in Svarita has the same frequency as the Udatta, and the later low pitch in Svarita has the same frequency as Anudatta.
The Paniniya Shiksha has this verse (based on which, I think, Srirama Sharma has given the Svara-pitch mappings) -
उदात्ते निषादगान्धारावनुदात्त ऋषभधैवतौ।
स्वरितप्रभवा ह्येते षड्जमध्यमपञ्चमाः॥
My understanding is that this verse corresponds to the following mapping on the musical scale, with two notes given for each Svara (four = 2 x 2 for Svarita)
Saa - Svarita pitch (after the initial half-instant)
Re - Anudaatta pitch
Ga - Udaatta pitch
Ma - Svarita pitch (initial half-instant)
Pa - Svarita pitch 2 (after the initial half-instant)
Dha - Anudaatta pitch 2
Ni - Udaatta pitch 2
Saa - Svarita pitch 2 (initial half-instant)
For more on this, you may want to refer works on Vedic accent. Some good works in Hindi are Sauvarah by Dayananda Saraswati, Vaidika Svara Mimamsa by Yudhishthir Mimamsaka and Vaidika Svara Samiksha by Amarnath Shastri. They are available on scribd and DLI.