Using a Lubachevsky-Stillinger-like growth algorithm combined with biased SWAP Monte Carlo and transient degrees of freedom, we generate ultradense disordered jammed ellipse packings. For all aspect ratios $α$, these packings exhibit significantly smaller intermediate-wavelength density fluctuations and greater local nematic order than their less-dense counterparts. The densest packings are disordered despite having packing fractions $ϕ_{\rm J}(α)$ that are within less than 0.5% of that of the monodisperse-ellipse crystal [$ϕ_{\rm xtal} = π/(2\sqrt{3}) \simeq .9069$] over the range $1.25 \lesssim α\lesssim 1.4$ and coordination numbers $Z_{\rm J}(α)$ that are within less than 0.5% of isostaticity [$Z_{\rm iso} = 6$] over the range $1.3 \lesssim α\lesssim 2.0$. Lower-$α$ packings are strongly fractionated and consist of polycrystals of intermediate-size particles, with the largest and smallest particles isolated at the grain boundaries. Higher-$α$ packings are also fractionated, but in a qualitatively-different fashion; they are composed of increasingly-large locally-nematic domains reminiscent of liquid glasses.