In the work called "108 Vaishnavaite divya desams" by M.S.Ramesam, the author says the following about the Nachiyar tirukoil mahatyam:
"The greatness of this divya desam is related in Brahmanda purana in a dialogue between sounaka rishi and Bhrigu Maharishi (Chapters 1 to 11 related Srinivasa Kshetra mahatyam)"
The author also says that, "the glory of this kshetra is mentioned in Bhayishttora purana, through Brahma Narada samvadam". I think, you have already mentioned about the Bhavishyottara purana.
The author further elaborates on the story of the Kshetra.
So, if you can check these references, you might find some answer, hopefully