The Kepler mission revealed hundreds of systems with multiple transiting planets, which provide key insights into the correlations within planetary systems and their architectures if the detection biases are properly accounted for. In He, Ford, & Ragozzine (2019, 2020), we developed an advanced forward model (SysSim) to infer the intrinsic distributions of planetary systems around FGK dwarfs, by modeling the Kepler detection efficiency and comparing simulated catalogs to the Kepler catalog. We showed that planetary systems around FGK dwarfs are clustered in periods and in sizes, the fraction of stars with planets (with Rp > 0.5REarth and 3d < P < 300d) increases towards later type (cooler) stars, and the observed multiplicity distribution can be well matched by two populations consisting of a low and a high mutual inclination component (a Kepler dichotomy). Here, I will present a new model to show that a broad, multiplicity-dependent distribution of eccentricities and mutual inclinations arising from systems at the angular momentum deficit (AMD) stability limit can also reproduce the observed populations. Systems with intrinsically more planets have lower eccentricities and mutual inclinations. For each intrinsic multiplicity count, the distributions of eccentricities and mutual inclinations are close to lognormal, instead of the previously assumed Rayleigh distributions. This trend with multiplicity arises from the dependence of the critical AMD on the minimum period ratio in the system, as systems with tightly-spaced planets must have low AMD in order to remain stable. We also find evidence that intrinsic single planets have higher eccentricities than multi-planet systems, although their distribution is not well constrained. I will show that there is evidence for these trends with multiplicity in the Kepler distributions of circular-normalized transit durations and transit duration ratios. Our code for simulating (intrinsic and observed) planet catalogs is public and can be used to inform RV follow-up efforts in the search for additional non-transiting companions in systems with transiting planets (such as those observed from the TESS mission).