Expanding on this theme of early strikes, a few things I have read over the years would have these early strikes looked out in a different light, although not true proofs they are referred to in several books to be select in production and therefore of similar quality to proof coinage and in some cases as 'specimen'.
These coins would probably be used in gifts and for marketing showing quality and detail, most commonwealth or dependent countries had coinage struck by the Royal Mint, some independent countries did also.
There are also pyx records of currency coinage undergoing the same scrutiny as proof and precious metal coinage.
I would reference Pecks, and Gruber before, with regard to Copper Pennies and Halfpenny references following his listings, recorded as bronzed currency coinage, and would cite the Colin Adams collection for numerous examples.
Hocking with regard reference to coinage struck for record, usually regarded as Proof.
Montagu with reference to CP1857 Proof, slabbed as 'Proof like' by NGC.
I am sure collectors of other denominations could come forward with examples of their own.
This would then bring about the question, which is rarer, the Specimen or the Proof.
1839 Proof sets were struck on order up until the 1853 set became available, the 1839 Halfpenny is the same Obv die as used on Jersey currency coinage of that date, no currency Halfpennies were struck for the UK in that year, and maybe once initial orders had been satisfied the dies were used for that purpose.
This caused 1841 Halfpenny and Penny replacing the 1839 Coppers within the sets, and for a short period, the the 1841 and 1843 Halfpennies dies were adjusted to 1839,
It is possible a similar action was initiated, maybe achieved on the Penny, Bramah references a 1841 copper penny with a crescent under the 4, the beginning of an 8, or just maybe a 3.