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We compare literature data for the isotopic ratios of Zr, Sr, and Ba from analysis of single meteoritic stardust silicon carbide (SiC) grains to new predictions for the slow neutron-capture process (the s process) in metal-rich asymptotic giant branch (AGB) stars. The models have initial metallicities Z = 0.014 (solar) and Z = 0.03 (twice-solar) and initial masses 2 - 4.5 Msun, selected such as the condition C/O>1 for the formation of SiC is achieved. Because of the higher Fe abundance, the twice-solar metallicity models result in a lower number of total free neutrons released by the 13C({\alpha},n)16O neutron source. Furthermore, the highest-mass (4 - 4.5 Msun) AGB stars of twice-solar metallicity present a milder activation of the 22Ne({\alpha},n)25Mg neutron source than their solar metallicity counterparts, due to cooler temperatures resulting from the effect of higher opacities. They also have a lower amount of the 13C neutron source than the lower-mass models, following their smaller He-rich region. The combination of these different effects allows our AGB models of twice-solar metallicity to provide a match to the SiC data without the need to consider large variations in the features of the 13C neutron source nor neutron-capture processes different from the s process. This raises the question if the AGB parent stars of meteoritic SiC grains were in fact on average of twice-solar metallicity. The heavier-than-solar Si and Ti isotopic ratios in the same grains are in qualitative agreement with an origin in stars of super-solar metallicity because of the chemical evolution of the Galaxy. Further, the SiC dust mass ejected from C-rich AGB stars is predicted to significantly increase with increasing the metallicity., Comment: 40 pages, 7 figures, 1 table. Accepted for publication on Geochimica Cosmochimica Acta