I will try to answer this question based on Dating of Mahabharat.
Shukla Ekadashi of Gita Jayanti is accepted in Puranas.
However Mahabharata does not give the Tithi/Nakshatra of Gita Jayanti. It simply says that the last war day (18) must be a Shravana nakshatra day and it must be an Amavasya or very close to it(K14 leading into Amavasya). Hence first war day must be Rohini/Mrigasira
And the Tithi of first war day must be Shukla Paksha 13/14
Hence first war day according to legend is either Shukla Paksha 13 according to calculation and backed up by Kane and others (source is Anumana from Mahabharata text) or Shukla paksha 11 according to tradition. In any case the war cannot start on an Amavasya as per what is said by Nilesh Oak (some others also claim this and is completely wrong)
Verse from Udyoga Parva 140:18 quoted as evidence foe starting war on Amavasya actually simply mentions that war preparedness is to be commenced at that time and in any case 7 days is too short a time for Mahabharata war to happen (according to the verse war preparations are to be started in 7 days from Karna Krishna Samvada)
Source : Here is the paper by Manish Pandit showing 6 major points of failure of 1432BCE including major timelines, eclipses, Saturn and Mars.
Chapter 11 of MM Pandit's book clearly shows the Moon in Rohini at Midday. "Sharadante Himagame" issue is faced by all 3KBCE dates.