ABSTRACT The microphysics of ∼ GeV cosmic ray (CR) transport on galactic scales remain deeply uncertain, with almost all studies adopting simple prescriptions (e.g. constant diffusivity). We explore different physically motivated, anisotropic, dynamical CR transport scalings in high-resolution cosmological Feedback In Realistic Environment (FIRE) simulations of dwarf and ∼L* galaxies where scattering rates vary with local plasma properties motivated by extrinsic turbulence (ET) or self-confinement (SC) scenarios, with varying assumptions about e.g. turbulent power spectra on un-resolved scales, Alfvén-wave damping, etc. We self-consistently predict observables including γ-rays (Lγ), grammage, residence times, and CR energy densities to constrain the models. We demonstrate many non-linear dynamical effects (not captured in simpler models) tend to enhance confinement. For example, in multiphase media, even allowing arbitrary fast transport in neutral gas does not substantially reduce CR residence times (or Lγ), as transport is rate-limited by the ionized WIM and ‘inner CGM’ gaseous halo (104–106 K gas within $\lesssim 10\!-\!30\,$ kpc), and Lγ can be dominated by trapping in small ‘patches’. Most physical ET models contribute negligible scattering of ∼1–10 GeV CRs, but it is crucial to account for anisotropy and damping (especially of fast modes) or else scattering rates would violate observations. We show that the most widely assumed scalings for SC models produce excessive confinement by factors ≳100 in the warm ionized medium (WIM) and inner CGM, where turbulent and Landau damping dominate. This suggests either a breakdown of quasi-linear theory used to derive the CR transport parameters in SC, or that other novel damping mechanisms dominate in intermediate-density ionized gas.