  In order to unravel the present situation of the PBH overproduction problem,
our study emphasizes the critical role played by the equation of state (EoS)
parameter $w$ within the framework of effective field theory (EFT) of
non-singular bounce. Our analysis focuses on a wide range of EoS parameter
values that are still optimal for explaining the latest data from the pulsar
timing array (PTA). As a result of our study, the most advantageous window,
$0.31 \leq w \leq 1/3$, is identified as the location of a substantial PBH
abundance, $f_{\rm PBH} \in (10^{-3},1)$ with large mass PBHs, $M_{\rm PBH}\sim
{\cal O}(10^{-7}-10^{-3})M_{\odot}$, in the SIGW interpretation of the PTA
signal. When confronted with PTA, we find that the overproduction avoiding
circumstances are between $1\sigma-2\sigma$, while the EoS parameter lies
inside the narrow window, $0.31<w\leq 1/3$. We propose a
regularized-renormalized-resummed (RRR) scalar power spectrum that is large
enough to produce EoS dependent scalar generated gravitational waves compatible
with PTA evidence, while satisfying the perturbativity, causality, and
unitarity criteria, within the range of $0.88 \leq c_{s} \leq 1$.
