The authors make a reasonable case for their preferred date. However, in the absence of additional historical data, theirs is simply a hypothesis. (Didn't we recalibrate the calendar in the 18th century, anyway, so that "April 3" is no longer what it once was?) It may be that we will not be able to identify the date, just as we may never know for certain where Andrew Jackson was born or who Abraham Lincoln's father was.
They also didn't bother to make the case that knowing the date is important. I don't see what it would add to our present sure knowledge that there WAS such a date.
I believe the crucifixion occurred on April 9th 32 AD, (which actually was a Wednesday that year)
And while it doesn’t matter for our salvation, it was important as a witness to Israel (at that time) because they did not know ‘the time of their visitation’ and were held accountable for not knowing, being the precise fulfillment of the timing of what Daniel (Chapter 9) was told were the two conditions to count for the 70 sevens (weeks) Prophecy (at 69 weeks, or 483 years) as occurring counting from March 14th, 445 BC to the arrival of the Messiah to be cutoff, (but actually it was 62 sevens, or 434 years counted not 69 as they rejected 7 weeks or 49 years)
And then additionally standing as a witness of the ‘Sign of Jonah’ to this very day, which Jesus alluded, for anyone that would care to consider it, as it set the date requiring ‘three days and three nights’ from the 14th of Nisan to the 17th of Nisan,