We present Spitzer Space Telescope observations of 11 regions south-east (SE) of the Bright Bar in the Orion Nebula, along a radial from the exciting star θ1 Ori C, extending from 2.6 to 12.1 arcmin. Our Cycle 5 programme obtained deep spectra with matching Infrared Spectrograph (IRS) short-high (SH) and long-high (LH) aperture grid patterns. Most previous IR missions observed only the inner few arcmin (the ‘Huygens’ Region). The extreme sensitivity of Spitzer in the 10–37 μm spectral range permitted us to measure many lines of interest to much larger distances from θ1 Ori C. Orion is the benchmark for studies of the interstellar medium, particularly for elemental abundances. Spitzer observations provide a unique perspective on the neon and sulphur abundances by virtue of observing the dominant ionization states of Ne (Ne+, Ne++) and S (S++, S3 +) in Orion and H II regions in general. The Ne/H abundance ratio is especially well determined, with a value of (1.02 ± 0.02) × 10−4 or in terms of the conventional expression, 12 + log(Ne/H) = 8.01 ± 0.01. We obtained corresponding new ground-based spectra at Cerro Tololo Inter-American Observatory (CTIO). These optical data are used to estimate the electron temperature, electron density, optical extinction and the S+/S++ ionization ratio at each of our Spitzer positions. That permits an adjustment for the total gas-phase sulphur abundance because no S+ line is observed by Spitzer. The gas-phase S/H abundance ratio is (7.68 ± 0.25) × 10−6 or 12 + log(S/H) = 6.89 ± 0.02. The Ne/S abundance ratio may be determined even when the weaker hydrogen line, H(7–6) here, is not measured. The mean value, adjusted for the optical S+/S++ ratio, is Ne/S =13.0 ± 0.2. We derive the electron density (Ne) versus distance from θ1 Ori C for [S III] (Spitzer) and [S II] (CTIO). Both distributions are for the most part decreasing with increasing distance. The values for Ne[S II] fall below those of Ne[S III] at a given distance except for the outermost position. This general trend is consistent with the commonly accepted blister model for the Orion Nebula. The natural shape of such a blister is concave with an underlying decrease in density with increasing distance from the source of photoionization. Our spectra are the deepest ever taken in these outer regions of Orion over the 10–37 μm range. Tracking the changes in ionization structure via the line emission to larger distances provides much more leverage for understanding the far less studied outer regions. A dramatic find is the presence of high-ionization Ne++ all the way to the outer optical boundary ∼12 arcmin from θ1 Ori C. This IR result is robust, whereas the optical evidence from observations of high-ionization species (e.g. O++) at the outer optical boundary suffers uncertainty because of scattering of emission from the much brighter inner Huygens Region. The Spitzerspectra are consistent with the Bright Bar being a high-density ‘localized escarpment’ in the larger Orion Nebula picture. Hard ionizing photons reach most solid angles well SE of the Bright Bar. The so-called Orion foreground ‘Veil’, seen prominently in projection at our outermost position 12 arcmin from θ1 Ori C, is likely an H II region–photo-dissociation region (PDR) interface. The Spitzer spectra show very strong enhancements of PDR lines –[Si II] 34.8 μm, [Fe II] 26.0 μm and molecular hydrogen – at the outermost position