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It has been proposed, and confirmed by multiple observations, that disks around low mass stars display a molecule-rich emission and carbon-rich disk chemistry as compared to their hotter, more massive solar counterparts. In this work, we present JWST Disk Infrared Spectral Chemistry Survey (JDISCS) MIRI-MRS observations of the solar-mass star DoAr 33, a low-accretion rate T Tauri star showing an exceptional carbon-rich inner disk. We report detections of H$_2$O, OH, and CO$_2$, as well as the more complex hydrocarbons, C$_2$H$_2$ and C$_4$H$_2$. Through the use of thermochemical models, we explore different spatial distributions of carbon and oxygen across the inner disk and compare the column densities and temperatures obtained from LTE slab model retrievals. We find a best match to the observed column densities with models that have carbon enrichment, and the retrieved emitting temperature and area of C$_2$H$_2$ with models that have C/O $=$ 2$-$4 inside the 500 K carbon-rich dust sublimation line. This suggests that the origin of the carbon-rich chemistry is likely due to the sublimation of carbon rich grains near the soot line. This would be consistent with the presence of dust processing as indicated by the detection of crystalline silicates. We propose that this long-lived hydrocarbon rich chemistry observed around a solar-mass star is a consequence of the unusually low M-star-like accretion rate of the central star, which lengthens the radial mixing timescale of the inner disk allowing the chemistry powered by carbon grain destruction to linger., Comment: 17 pages, 12 figures, 5 tables, 5 appendices (9 additional pages, 10 additional figures). Accepted for publication in ApJ