A number of coin catalogues report Franklin Mint-struck matte sets for the Solomon Islands for the years 1977, 1978, 1979, 1980, 1981 and 1983 with a mintage of 6,000 for each year. The source for these mintages is unstated but it seems very unlikely that any Solomon Islands matte sets were ever struck.
Besides the lack of any sightings of any Solomon Islands matte sets, the mintage of 6,000 in each year is incredibly high, especially for 1983 when no more than a few hundred special uncirculated and proof sets were struck. Also, as the popularity of Franklin Mint products declined, so did the popularity of the matte sets - for example, no matte sets were struck at all by the Franklin Mint for Malta in 1982: only special uncirculated and proof sets.
Unfortunately the Franklin Mint's records seem to be least, so the reported mintages may remain a mystery, but it possible that a Solomon Islands matte set may appear.
In 2019 on the Coin Community forums, a user posted images of an 1884 Straits Settlements 1c which appeared to have been struck with a British Honduras 1c obverse die - the first reporting of such a mule. Both denominations were struck at the Royal Mint in London.
While very similar at first glance, the two different renditions of the Leonard Charles Wyon obverse have a number of small differences - on the Straits Settlements obverse the denticles are short; the hair ribbon almost touches the N in QUEEN and the hair curls behind the ear point down while on the British Honduras obverse, the denticles are long; the hair ribbon is away from the N in QUEEN and the hair curls behind the ear point up. The British Honduras obverse is also slightly smaller at 28.35mm compared to the Straits Settlements obverse at 29mm.
The circumstances in which the mule was struck will probably never be known, but given the extreme similarity of the two obverse dies, an innocent mix-up of dies is the most likely scenario, especially considering that it was the first time the Royal Mint had struck Straits Settlements and British Honduras 1c pieces. A die shortage is also possible - if no Straits Settlements obverse dies were currently available, using a similar substitute die may have been acceptable, though this is less likely given that British Honduras 1c pieces were first struck in 1885. This is not to say that British Honduras obverse working dies were not available in large quantities in 1884, but it seems unlikely considering the British Honduras 1c denomination was first struck and released in 1885.
It remains to be seen if any further examples come to light, but given the subtle difference it is very likely that other examples remain to be discovered.
New Zealand does not have its own mint so the tasks of circulating coin production and mint and proof set production is outsourced. In many years the circulating coins have been struck by a different mint to the mint and proof set coins. Although New Zealand's decimal currency was launched in 1967, it wasn't until 1971 that different mints were responsible for striking circulating and set coins.
In 1971 the Royal Australian Mint in Canberra struck New Zealand's circulating coins while the Royal Mint in Llantristant struck New Zealand's mint and proof sets. The two mints used slightly different obverse dies so it is possible to differentiate the circulating and set coins: on the circulating coins, the 1 in the date has angled serifs at its base, while on the set coins, the 1 in the data has very slight (almost no) serifs as its base.
The Franklin Mint produced uncirculated and proof sets (and reportedly matte sets) for the Solomon Islands from 1977 to 1983. By 1983, the interest in Franklin Mint collectables was clearly waning - all 1983 sets are rate and sets were only produced for a handful of countries in 1984 before the Franklin Mint ceased to produce coins altogether. It is believed that only uncirculated and proof sets were produced for the Solomon Islands in 1983, though matte sets have been reported. It is also believed they were struck to order i.e. the sets were advertised; buyers registered their interest and sets were struck for all those who registered interest.
The number of 1983 uncirculated and proof sets struck is not known, though figures of 192 and 200 have been put forward for the number of uncirculated sets. In previous years the number of proof sets higher so the same would likely be true for 1983 as well. Regardless, the sets are rare and it is probable that no more than a couple of hundred of each were struck. Unfortunately the records for later-issue Franklin Mint coins do not appear to have been released so will probably remain unknown.
The Cook Islands is a small nation and like many small nations doesn't have massive demand for new coins each year - in the 22 years of the Cook Islands having its own coinage, circulating coins were only struck in eight different years. Uncirculated sets and proof sets were struck in a number of years when no circulating coins were issued as well, including the final year of Cook Islands coinage - 1994.
Although the reported mintages of the 1994 Cook Islands coin sets - 20,000 uncirculated sets and 200 proofs sets - are comparatively high - the sets are very rare. The sets were all struck by the Royal Australian Mint in Canberra but it is unknown where the sets were marketed, or if all of the sets ended up being issued.