I think it's safe to dismiss the "traditional dates" as probably having a political origin.
Jainism used to be a much bigger element in Indian religious life than now ~ just like Buddhism.
Here's a thought for you ~ being a Jain carries with it all the burdens of the highest levels of Christian morality with none of the benefits.
The last of the Tirthankars i.e Mahavira pre-dates Buddha, hardly within his "lifetime".
The "traditional dates" are always a matter of contention and is so in every religion including the Judeo-Christian ones.
Jainism is bigger then what Buddhism is in modern India and at no point in history did it assume any greater space in Indian religious life. It always had a fringe existance.
"being a Jain carries with it all the burdens of the highest levels of Christian morality with none of the benefits."
Morality itself is a burden or a benefit depending on how you see it. What other benefit are you talking about?