The binding energy curve, again in wikipedia, shows iron as the one with the smallest binding energy per nucleon. Though in the table, the following is stated:
56Fe has the lowest nucleon-specific mass of the four nuclides listed in this table, but this does not imply it is the strongest bound atom per hadron, unless the choice of beginning hadrons is completely free. Iron releases the largest energy if any 56 nucleons are allowed to build a nuclide—changing one to another if necessary, The highest binding energy per hadron, with the hadrons starting as the same number of protons Z and total nucleons A as in the bound nucleus, is 62Ni. Thus, the true absolute value of the total binding energy of a nucleus depends on what we are allowed to construct the nucleus out of. If all nuclei of mass number A were to be allowed to be constructed of A neutrons, then Fe-56 would release the most energy per nucleon, since it has a larger fraction of protons than Ni-62. However, if nucleons are required to be constructed of only the same number of protons and neutrons that they contain, then nickel-62 is the most tightly bound nucleus, per nucleon.
One sees that there is a leeway when constructing models in end of the universe scenaria. There is so much speculation in the time lines. Observation tells us that Ni-62 is not abundant, while Fe is. It seems that in the sequence of supernova explosions iron wins out; according to the quote above, this would mean that it is the number of nucleons that is important and the charges statistically arrange themselves.
Anyway, in a continuously expanding universe with a stable proton it is hard to see how the expanding gases of Helium and Hydrogen can tunnel into anything as they expand so that "all matter" would end up as Fe or Ni atoms .
Not to worry, the proton will decay according to most current models of particle physics anyway.