This paper investigates molecular-scale polymer mechanical deformation during large-strain squeeze flow of polystyrene (PS) films, where the squeeze flow gap is close to the polymer radius of gyration (R-g). Stress-strain and creep relations were measured during flat punch indentation from an initial film thickness of 170 nm to a residual film thickness of 10 mm in the PS films, varying molecular weight (M-w) and deformation stress rate by over 2 orders of magnitude while temperatures ranged from 20 to 125 degrees C. In stress-strain curves exhibiting an elastic-to-plastic yield-like knee, the response was independent of M-w, as expected from bulk theory for glassy polymers. At high temperatures and long times sufficient to extinguish the yield-knee, the mechanical response M-w degeneracy was broken, but no molecular confinement effects were observed during thinning. Creep measurements in films of 44K M-w were well-approximated by bulk Newtonian no-slip flow predictions. For extrusions down to a film thickness of 10 mm, the mechanical relaxation in these polymer films scaled with temperature similar to Williams-Landel-Ferry scaling in bulk polymer. Films of 9000K M-w, extruded from an initial film thickness of 2R(g) to a residual film thickness of 0.5R(g), while showing stress-strain viscoelastic response similar to that of films of 900K M-w, suggestive of shear-thinning behavior, could not be matched to a constitutive flow model. In general, loading rate and magnitude influenced subsequent creep extrusion depth of high-M-w films, with deeper final extrusions for high loading rates than for low loading rates. The measurements suggest that, for high-resolution nanoimprint lithography, mold flash or final residual film thickness can be reduced for high strain and strain rate loading of high-M-w thin films.