The iron-peak elements are mostly the product of alpha capture reactions onto nuclei that begin with a similar number of neutrons and protons ($Z = N$).
The nuclear burning associated with carbon and oxygen (in type Ia supernovae) or silicon (in the cores of massive stars at the ends of their lives) is very fast or even explosive. The important reactions in determining the immediate final products are those that proceed on fast timescales.
In these cases, there is a competition between alpha capture and photodisintegration with the constraint that $Z \simeq N$, since weak, flavour-changing reactions are generally too slow to move the neutron/proton ratio far from unity before an equilibrium has been reached between alpha capture and photodisintegration.
Subject to these constraints, then Ni56 turns out to be the most stable nucleus. Further alpha captures to Zn60 (or beyond) are not favored, because these nuclei have lower binding energy and the higher temperatures that would be required to overcome the greater coulomb barrier results in photodisintegration to smaller nuclei.
Hence there is no easy route to Ni62.
The fact that Fe56 dominates the iron-peak element abundances that are seen in the atmospheres of stars and the interstellar medium is because the Ni56 in supernovae ejecta decays to Co56 and then Fe56 on half-lives of 6 and 77 days respectively. Inside the dense core of a massive star then electron capture by Ni56 can be more rapid, but still results in Fe56.