I have discussed this with Ven Dhirasekera Dhammavihari, one of the foremost Pali scholars of his generation, who was present at the 6th Council, as well as with Major Surathat Bunnag, founder of the Dhamma Society, whose mother was present, and who sponsored the Mahasangiti edition in her honor.
At the Council itself, the main proceedings were run by the Burmese monks, with Ven Vicittasarabhivamsa reciting in response to questions of Mahasi Sayadaw. It seems that little was done in terms of debating and resolving the issues between the different versions.
No detailed records or methods appear to have survived, but according to Ven. Dhammavihari the Burmese, Thais, and Sinhalese each did their own recensions. Thus the 6th Council edition is largely a confirmation and update of the Burmese 5th Council edition, and as such, preserves the characteristic Burmese Pali spellings. Also, certain additions to the text, such as adding the long section on the four noble truths to MN 10 Satipatthana, were retained from the 5th Council edition.
According to Major Surathat, this text was printed in the first edition of the 6th Council text in Myanmar. However, he says that following the unrest in Burma in the early 60s, the second edition was by mistake a simple reprint of the old 5th Council edition. Subsequent editions, including the VRI digital edition, were based on this. I have not been able to confirm this independently.
The revision made by Major Surathat's Dhamma Society and published as the Mahasangiti edition was based on the VRI text. However it used the first edition—that is, the actual 6th Council text—as the mainline reading.
I believe, although again I have not confirmed it independently, that the Buddha Jayanthi edition in Sinhalese script is descended from the text redacted by the Sri Lankan monks at the 6th Council. This has subsequently been digitized independent of the VRI/Mahasangiti text. I am not sure if the Thai version was digitized.