  The framework of trans-Planckian asymptotic safety has been shown to generate
phenomenological predictions in the Standard Model and in some of its simple
new physics extensions. A heuristic approach is often adopted, which bypasses
the functional renormalization group by relying on a parametric description of
quantum gravity with universal coefficients that are eventually obtained from
low-energy observations. Within this approach a few simplifying approximations
are typically introduced, including the computation of matter renormalization
group equations at 1~loop, an arbitrary definition of the position of the
Planck scale at $10^{19}$ GeV, and an instantaneous decoupling of gravitational
interactions below the Planck scale. In this work we systematically
investigate, both analytically and numerically, the impact of dropping each of
those approximations on the predictions for certain particle physics scenarios.
In particular we study two extensions of the Standard Model, the gauged $B-L$
model and the leptoquark $S_3$ model, for which we determine a set of
irrelevant gauge and Yukawa couplings. In each model, we present numerical and
analytical estimates of the uncertainties associated with the predictions from
asymptotic safety.
