Previously, we provided a novel systematization of alpha-decaying even-even nuclei starting with the classically adopted mechanism (Yarman et al., Eur. Phys. J. A 52, 140 (2016)). The decay half-life of an alpha-decaying nucleus was framed so that i) the alpha-particle is taken at the outset to be born inside the parent nucleus with a given probability, ii) where it then keeps on bouncing off of the barrier of the parent nucleus till iii) it finally tunnels through the barrier. Knowing beforehand the measured decay half-life, we have taken into consideration, as a parameter, the probability of the alpha-particle being first born within the parent before it is emitted. We thence developed a scaffold based on shell properties of families composed of alike even-even nuclei. Nevertheless, our model allows us to incorporate any alpha-decaying nuclei, and along this line, we present a follow-up systematization of even-odd nuclei, with cases of odd-even and odd-odd alpha-decaying nuclei pending to be considered in a separate contribution. Notwithstanding, we make an effort herein to expand our approach to investigate the effect of "pairing" (e.g., when a number of nucleons in the given nucleus becomes an even number, instead of the initial odd number, due to the addition of at least one neutron). Our results show that "pairing", as expected, definitely increases the stability of the given nucleus.