I see. So instead of making up a specific date, which, in early times, would have been completely unverifiable one way or another, but which would have lended veracity to the Story, your conspirators purposefully chose to leave the date ambiguous?
You can't stay out of your own way. Your arguments are now contradicting your point of view. Isn't it more plausible that rather than choosing to omitt a date all four authors neglected to include one, because it just wasn't important to them?
The date of the most important event in history (according to them) was unimportant?