We present a new suite of cosmological zoom-in hydrodynamical ($\approx 20\, \mathrm{pc}$) simulations of Milky-Way mass galaxies to study how a varying mass ratio for a Gaia-Sausage-Enceladus (GSE) progenitor impacts the $z=0$ chemodynamics of halo stars. Using the genetic modification approach, we create five cosmological histories for a Milky-Way-mass dark matter halo ($M_{200} \approx 10^{12} \, M_\mathrm{\odot}$), incrementally increasing the stellar mass ratio of a $z\approx2$ merger from 1:25 to 1:2, while fixing the galaxy's final dynamical, stellar mass and large-scale environment. We find markedly different morphologies at $z=0$ following this change in early history, with a growing merger resulting in increasingly compact and bulge-dominated galaxies. Despite this structural diversity, all galaxies show a radially-biased population of inner halo stars like the Milky-Way's GSE which, surprisingly, has a similar magnitude, age, $\rm [Fe/H]$ and $\rm [\alpha/Fe]$ distribution whether the $z\approx2$ merger is more minor or major. This arises because a smaller ex-situ population at $z\approx2$ is compensated by a larger population formed in an earlier merger-driven starburst, with both populations strongly overlapping in the $\rm [Fe/H]-\rm [\alpha/Fe]$ plane. Our study demonstrates that multiple high-redshift histories can lead to similar $z=0$ chemodynamical features in the halo, highlighting the need for additional constraints to distinguish them, and the importance of considering the full spectrum of progenitors when interpreting $z=0$ data to reconstruct our Galaxy's past.