We present panchromatic optical + near-infrared (NIR) + mid-infrared (MIR) observations of the intermediate-luminosity Type Iax supernova (SN Iax) 2024pxl and the extremely low-luminosity SN Iax 2024vjm. JWST observations provide unprecedented MIR spectroscopy of SN Iax, spanning from +11 to +42 day past maximum light. We detect forbidden emission lines in the MIR at these early times while the optical and NIR are dominated by permitted lines with an absorption component. Panchromatic spectra at early times can thus simultaneously show nebular and photospheric lines, probing both inner and outer layers of the ejecta. We identify spectral lines not seen before in SN Iax, including [Mg ii] 4.76 μm, [Mg ii] 9.71 μm, [Ne ii] 12.81 μm, and isolated O i 2.76 μm that traces unburned material. Forbidden emission lines of all species are centrally peaked with similar kinematic distributions, indicating that the ejecta are well mixed in both SN 2024pxl and SN 2024vjm, a hallmark of pure deflagration explosion models. Radiative transfer modeling of SN 2024pxl shows good agreement with a weak deflagration of a near-Chandrasekhar-mass white dwarf, but additional IR flux is needed to match the observations, potentially attributable to a surviving remnant. Similarly, we find SN 2024vjm is also best explained by a weak deflagration model, despite the large difference in luminosity between the two supernovae. Future modeling should push to even weaker explosions and include the contribution of a bound remnant. Our observations demonstrate the diagnostic power of panchromatic spectroscopy for unveiling explosion physics in thermonuclear supernovae.