Balaram had gone on a Yatra as he did not wish to witness the war between Kurus and Pandavas. He came back from the Yatra on the last day of the war to umpire the Gadayuddha between Bheem and Duryodhan. He said that I left for yatra on Pushya nakshatra and have come back on Shravan (Nakshatra) and my Yatra was of 42 days. Between Pushya and Shravan 42 days are correctly accounted for (27 + 14) .
If this statement by Balaram is accepted as correct, the Nakshatra on 18th day was Shravan and the one on the first day of war had to be Mruga. If the first day also needs to be an Amavasya, then Sun and Moon on that day have to be in Mruga.
In 5561 BCE, according to Shri. Oak Sun and Moon were at Jyeshtha on 16th Oct. Sun would have been in Mruga, 13 nakshatras back, in April 5561 BCE or later, in April 5560 BCE. In April 5561 or 5560 BCE, was there any Amavasya in Mruga ? Even if there was, the season wont be correct. It seems 5561BCE and Shravan on 18th day cannot be reconciled at all if first day it taken as 16th Oct.5561BCE.( Will there be any year, in which there was an Amavasya in Mruga, which was also in an appropriate season for war? It would be necessary that the Mruga Amavasya should be a little after Autumnal Equinox )
If, on the other hand, we give up Amavasya and agree that first day of war should be on Mruga Nakshatra, i. e. moon in Mruga, it would be 14-15 days after 16th Oct, as Moon (and Sun) was in Jyeshtha on 16th Oct. So the first day becomes 31st October which would be a day after the end of the exceptionally short lunar fornight of 13 days and so Vyasa would be justified in referring to it in his talk with Dhritarashtra on the previous day! Is Shri. Oak willing to give up Amavasya? Most of the so called astronomical observations would be equally true or untrue for 31st Oct. as for 16th Oct. Of course the war then begins on a Purnima. It will also solve the problem of late moonrise of 14th day! The day will be 13th or 14th in Krishna Paksha! The pitch darkness on 7th and 8th day after sunset would also be natural, being krishnapaksha.
Shri. Oak has bypassed the anomaly of 42 days by assuming ‘श्रवणे’ to mean ‘on hearing’. A novel approach but does not hold water. The word should have been ‘श्रुत्वा’ for that purpose, followed by words to say on hearing what. Any rational reason why Vyasa would use a wrong word? Sanskrit does not permit you to make fanciful interpretations. Shri Oak is well aware of the correct meaning of श्रवणे. (Remember मघास्वंगारको वक्रः श्रवणे च बृहस्पतिः?). Let us stick to that meaning.
My (fanciful) proposal - As time passed, Sarasvati tirthyatra got standardized as a 42 day yatra from Pushya to Shravan. Then, assuming that Balaram must have observed the rule, someone interpolated Pushya and Shravan in Mahabharat in Balaram’s mouth. What had actually taken place was only that Balaram came back from the yatra on 42nd day of yatra, just in time for witnessing the 18th day Gadayuddha between Bheem and Duryodhan. It may not have been a Shravan day at all!
I have read a Novel alternative explanation of this problem in a Marathi book by a reputed scholar, Prof. G. V. Kavishvar. Translation of the Marathi title (महाभारतातील गूढ रहस्ये) would be ‘Puzzles of Mahabharat’. It is an old book and handles many intricate problems. His solution in this case is simple. He proposed that the war was not fought continuously every day for 18 days. After every day of war there was a day of truce, when the warriors rested, tended to their injuries and planned new strategies. This continued until the 14th day when Jayadratha was killed by Arjuna. (Actually 27th day) The war did not stop with that or with the sunset or darkness but continued throughout the night with a short spell of resting when all were deeply tired and there was complete darkness also. But it resumed with moonrise and continued uninterrupted next day till Drona’s death (28th day). Thus the last day of war was not 18th but 34th day which matches with Shravan! He himself has of course stated that there is no direct evidence of the rest day in Mahabharat. Readers may find this an interesting proposal.