Some years ago, based on a reading of Muḥammad ʿAlam al-hudā, the son of Muḥsin Fayż Kāshānī and grandson of Mullā Ṣadrā, I suggested that the correct death date for Mullā Ṣadrā was 1045 AH and not 1050 AH as commonly understood, and that this was on the return from his seventh ḥajj in Basra and that his body was taken to Najaf to be buried in the precinct of the Imam's shrine.
Now an article has just recently been published that provides some further evidence and correction to my report. I am grateful to Alireza Asghari for alerting me to this and to sending me a copy.
The reference for the article is:
Ḥusayn Vāsiqī, "Safar-hā-yi ḥajj-i khāndān-i Fayż-i Kāshānī', Mīrās-i Shihāb, 76-77 (1394 Sh), 121-28
[This is the journal published by the Kitābkhāna-yi Marʿashī Najafī in Qum]
Vāsiqī cites two majmūʿa-s donated to the library by the descendants of Fayż that includes plenty of useful information about the family, in particular Majmūʿa 8446 in the hand of ʿAlam al-hudā and 8447 in the hand of his son Muḥammad Muḥsin 'Vafāʾ'. The information in MS 8447 is broadly based on MS 8446 and was already partially used by Sayyid Shihāb al-Dīn Marʿashī in the introduction to Maʿādin al-ḥikma fī makātib al-aʾimma (my source for the dating in the first place). In MS 8446, ʿAlam al-hudā notes that his grandfather died on his way to ḥajj in Baṣra in the year 1045 (so at the very least before Dhū-l-Qaʿda in that year). In MS 8447, his son Vafāʾ states that this was on his way to his second ḥajj (I have not checked references to his ḥajj pilgrimages in his own works but it's possible that I've overlooked them), and that his body was taken to be buried in Najaf in the courtyard to the left of the mausoleum of the Imam. Vafāʾ says that he heard this from some friends - and 'perhaps from my father'. Of course, it was ʿAllāma Sayyid Muḥammad Ḥusayn Ṭabāṭabāʾī and Sayyid Abū-l-Ḥasan Rafīʿī Qazvīnī (bi-riwāyat Seyyed Hossein Nasr) who said that he had died in Basra on his seventh ḥajj in 1050 AH and was buried there. Here is a piece that repeats the 1050 AH date but with the assertion of being buried in Najaf.
Here is the excerpt from the manuscript:
So perhaps not a huge point. It's a shame that there is little memory of this - the problem is that the books published on those buried in the precinct (such as this work) and the little map that you get from the shrine authorities only goes back 200 years at most. But then such works don't mention Sayyid Muḥammad Bāqir known as Mīr Dāmād, Mullā Ṣadrā's teacher and sometime Shaykh al-Islām of Iṣfahān under Shāh Ṣafī I, who was known to have died in Najaf on ziyāra with the Shah and been buried there (as the historical works mention). It would be great if scholars in Najaf could work further on those buried there in earlier periods.
So here is some evidence - and given that none of his works are dated later than 1044 AH - that suggests strong evidence for middle to late 1045 AH which approximates to the early months of 1636 CE.