The question of the numbered strikings was addressed by Graham Dyer, former curator at the RM Museum in a 1982 article entitled 'Numbered Strikings of Victorian Bronze Coins, 1860-1868'. Whilst people are unlikely to have this, the important points are laid out in Michael Gouby's 2000 publication 'The British Bronze Coinage, Pence, Halfpence and Farthings 1860-1869' whereby Dyer has shown the improper fractions seen on a few coins relate to the total tonnage of bronze to that point (larger number) and the tonnage of that denomination (smaller number). As the BM has an example of an 1864 farthing with 236/11 (P1872) and there is a penny with 237/134 (P1662), using the consecutive numbers as a total for bronze output in tons, we can deduce the tonnage of halfpennies to that point, as after 236 tons of bronze struck there had been 11 tons of farthings and (using 237/134 as a reference point) 133 tons of pennies. ie, the remainder is 92 tons of halfpennies.
Further to the above, the introduction to the publication gives a little history, including some useful snippets, summarised as follows:
Victoria was only happy with the portrait at the beginning of August 1860.
The mint was very busy at this time with gold and silver and didn't have the resources to produce the number of coins required for the changeover. Consequently they gave Watt a contract for 1720 tons (including all three denominations) in the first week of Sept. Production was underway at the Tower mint by the end of the month. On the 15th October, daily output of halfpennies and farthings was just over 150K - 50K short of the 200K target. The deficiency was due to too many dies breaking, with an average of 30000 strikes obtained instead of the usual average of 60000. There was a need to reduce the relief on all three denominations at this point. The farthing was done, the halfpenny was 'very nearly ready', but the pennies required a further alteration, so at this point were still not in production. Nor had Watt started production by the end of November. The beaded border created a problem, with flaws appearing in this area regularly.
Taking the above into consideration, it is hardly surprising there are fewer pennies extant than the other denominations for 1860.
Given the delay in getting the bronze coinage started, I would have thought they prepared 1860 dies for all three denominations. 1859 halfpennies and farthings are both scarce, and the halfpennies I have had of this date were all struck from old worn dies, whether 9 over 8 or not. So it is likely they intended to strike a good number of the smaller denominations in any case. As John pointed out, the halfpenny obverse was certainly used commercially.
It is beyond debate that they intended to change over to thinner, harder bronze coins earlier than they did, but as the decimal patterns of 1857-9 show, the bronze flans were prone to lamination. See below for the F689 edge. All 686s have this problem too. As these are both dated 1859, it is clear the problem was ongoing. Both are struck in bronze with a thickness of 1.5mm and are 27.5mm diameter. Freeman analysed the similar F686A to have 92.5% copper, 5% nickel, 2 % tin and 0.5% zinc, but this variation in alloy didn't cure the problem.
For those unaware of what the numbered coins refer to, please see attached 1866 halfpenny showing 405 behind the head and 138 in front, i.e. 405/138.