Agree that the question is interesting, but I am not so certain about the conclusions.
I agree that the Mk 45 is likely more accurate and has a higher ROF, but I am skeptical about how effective the 5"/127mm shells would be vs. the armour aboard the cruisers or the battlecruiser. One has to remember that warships designed and built in that era were expected to engage in gun duels. The Mk 45 would have out-ranged the guns fitted aboard the cruisers with a max effective range of ~24 km vs. ~13 km for the 6"/50 cal. Mk XI guns which IMO is one of the two factors which would have mattered. The other being how effective the 5"/127 mm shells would have been against the various thicknesses of armour. If the RNZN frigates could maintain a distance from the cruisers, then they would likely overcome the cruisers in time. The ROF difference I believe would work to to being negligible in the end, whilst the Mk 45's have a higher ROF (at least when using ready rounds, which could get exhausted after a few minutes) of up to 20 rounds/min, the cruisers themselves have more guns each with a ROF of 5-7 rounds/min. If a cruiser could manage to get three of their 6" guns to bear, that would be a ROF of 15-21 rounds/min and with three cruisers vs. two frigates... it easily be that the cruisers could manage a greater volume of fire, assuming they could get within range.
Similarly, I am not so certain that a Penguin AShM could manage to achieve a mission kill vs the battlecruiser, since the design again was from an era where naval gun battles were expected as well as there being significantly less of the modern sensors and electronics. No question that the 120 kg warhead would do damage, but I am much less certain that it could inflict enough damage, in critical areas of a warship from that era, that would effectively neutralize it. If the NZDF actually has any Penguin AShM that could be fired (there is some question of what the inventory is, what condition it is in, and whether or not NZ has ever actually test-fired it) then a max of two could be fitted at once. In order to effectively disable the main guns of the battlecruiser both normal and backup fire control positions would need to be disabled, and there would still be 16 4" guns fitted to the superstructure which could be used as well.
Such an engagement would come down to whether or not the RNZN could maintain the distance from the cruisers and battlecruiser, and would the stocks of ordnance be sufficient to hold out whilst damage was being inflicted. If the battlecruiser was able to close range with the RNZN frigates, then the contest would essentially be decided. The speed of the battlecruiser was quite close to that of the frigates, and the 12"/50 cal. Mk X guns had a range of ~18.5 km, so things would get quite dicey for the frigates. They would have little opportunity to fire the Mk 45's since they would need to be on a heading away from the battlecruiser in order to maintain the distance, which would put the Mk 45's out of a useful firing arc whilst there would be multiple potential firing arcs from the battlecruiser and cruisers.