I agree regarding the lack of scientific application. Personally, I feel the 1645s are likely to be over-represented due to the almost automatic illustration of any flat crown 1645 despite there only being a couple dozen or so. I did start to make a list of identifiable Newark siege pieces, but lost the will to live a few years ago. Whatever the distribution, there is no excessively large skew suggesting that coining took place continuously for months prior to the New Year, nor that coining only took place in (literally) a few days leading up to New Year. The actual periods when coins could have been struck are flexible to a point, as money of necessity only it would be made as a last resort after any available coin had been used. I think we can be confident that dated coins were struck in the appropriate year.
If there had to be a case made for an issue considerably earlier, that would have to be the flat crown pieces, but their relative rarity suggests a very short striking period. The two spellings of NEWARK(E) on the regular shillings might be indicative that shillings and ninepences with the terminal E were concurrent with the flat crown shillings. If so, one might be inclined to consider these were struck at a completely different time to those without the E. That would favour an early striking such as the arrival of Charles with a significant number of troops, thus requiring plate due to the immediate supplies of coin being insufficient. But the quid pro quo for any early output is a reduction in the length of time for late strikings, i.e.that would negate any lengthy striking period in Feb/March 1645 because I think we can reasonably assume similar survival rates for both 1645 and 1646, plus the spelling varieties.
The absence of many halfcrowns dated 1645 poses a bit of a conundrum. As the basic pay for a cavalryman, you would have expected a fairly even distribution across the dates. Was there a large supply of halfcrowns, yet no shillings? What also seems unlikely is that there would be a large output of shillings and ninepences relative to halfcrowns when the majority of Royalist troops by this time were mounted cavalry. Charles' infantry was decimated at Naseby, so you would have expected the halfcrown/shilling ratio to increasingly favour the former, if it did in fact change. If the spelling of Newark has any bearing, then it might be that coins without the E represent the striking period leading up to the surrender, in which case, the ratio of 1645 to 1646 Newark coins as a whole gives us the approximate split for the period leading up to and after the New Year.
The levies would have fallen on the inhabitants once the town was under siege with any Royalists taking refuge likely to be assessed in name only unless they were fortuitously ably to carry their wealth with them. I don't know if records exist for Newark covering the siege period, but those surviving at Chester record fortnightly assessments of £200 during the autumn months. However, there is no confirmation that these sums were actually collected in full. There is a record of a shortfall on one occasion. Again, at York, Slingsby records that there was no money or plate surviving towards the end.
So much we don't know that I wish we did.