When was Bhagavatam written by Vyasadeva?

From Bhagavata Mahatmya, Padma Purana, Uttara Khanda:

Saunaka asked, "O Suta Gosvami, when did Sukadeva recite the Bhagavatam to Pariksita, Gokarna to Dhundhukari, and the Kumaras to Narada Muni?"

Suta Gosvami replied, "About thirty years after Lord Krsna's departure to His abode, on the ninth day of the bright fortnight in the month of Bhadra, Sukadeva recited Bhagavatam to Pariksit. Two hundred years later in the month of Asadha, on the ninth day of the bright fortnight Gokarna recited Bhagavatam to Dhundhukari. Thirty years later, in the month of Karttika on the ninth day of the bright fortnight, the Kumaras recited it to Narada Muni."

SUMMARY

February 18, 3102 BCE (around): Krsna's disappearance, beginning of Kali Yuga (Thus Krsna was present for around 125+48 = 173 years)

30 years after i.e 3072 BC: Sukadeva Goswami speaks Bhadra Navami Bhagavatam to Maharaj Pariksit

200 years later i.e. 2872 BCE: Gokarna recited Bhagavatam to Dhundhukari on Asadha Navami

30 years later i.e. 2842 BCE: Kumaras recited to Narada Muni on Karttika Navami

Around 2000 BC: Suta Goswami recited to the sages at Naimisaranya (long after the battle of Kuruksetra)
[Jan: Suta Gosvami retold SB to sages in Naimisaranya at the end of yajna lasting for 1 000 years (SB 1.1.4) which started after the end of Kali yuga (SB 1.1.21, exact date not found in SB but as per SB 1.17.43-44p. after the death of Maharaja Pariksit, exact date again not in SB). Puranic Encyclopedia, entries Bharata II., Janamejaya I. and Pariksit I., say that Janamejaya became king in 3042 BCE (i.e. after the death of his father, Maharaja Pariksit). Thus the date of SB's retelling in Naimisaranya would be 2042 BCE.]

after 1000 BCE: Compiling of Mahabharata

500 BCE: Compiling of Ramayana

before 900 CE: Vyasadeva completed writing the 12 Canto of the Bhagavatam

The last three dates have been picked up from the Introduction of Sri Krsna-samhita by Srila Bhaktivinoda Thakura. He gives the date of the writing of the Srimad Bhagavatam as being around 900 AD in the opinion of modern scholars and goes on to give very foolproof evidences regarding this which the modern scholars give. Though Bhaktivinoda Thakura himself put a lot of effort into writing this Intro., he leaves it upto the reader to accept it or not.

And he writes while trying to figure out a date of compiling of the Bhagavatam as per the modern scholars:

"Now we will consider the modern scholars view on the date of the appearance of Srimad Bhagavatam, the jewel of all scriptures. Not understanding our statements, third-grade people may lose all faith and consider it a recent work. Therefore they should read this section..."