  We theoretically explore 2d moir\'e heterostructures in lattice-commensurate
magnetic fields as platforms for quantum simulation of a paradigmatic model of
non-Fermi liquid physics: a Fermi-surface coupled to a fluctuating gauge field.
In these moir\'e-Hofstadter (MH) systems, long-wavelength acoustic phonons
exhibit singular interactions with electrons analogous to those of electrons
with 2d gauge fields. This leads to a breakdown of Fermi-liquid theory at low
temperatures. We show that a combination of large moir\'e-unit cell size,
tunable Fermi-surface topology, and enhanced coupling to interlayer sliding
modes, enhance these effects by over many orders-of-magnitude compared to bulk
crystals, placing them within experimental reach. Though we find that the
asymptotic low-temperature non-Fermi liquid regime remains at prohibitively low
temperatures, striking precursor non-Fermi liquid signatures can be observed,
and we propose surface acoustic wave attenuation and quantum oscillation
transport experiments. We also study the motion of MH acoustic-polarons, which
we predict exhibit logarithmically diverging effective mass and unconventional
magnetic field scaling for scaling of cyclotron resonance frequency and quantum
oscillation amplitude.
