We have observed long-range spin-triplet supercurrents in Josephson junctions containing ferromagnetic (F) materials, which are generated by noncollinear magnetizations between a central Co/Ru/Co synthetic antiferromagnet and two outer thin F layers. Here we show that the spin-triplet supercurrent is enhanced up to 20 times after our samples are subject to a large in-plane field. This occurs because the synthetic antiferromagnet undergoes a "spin-flop" transition, whereby the two Co layer magnetizations end up nearly perpendicular to the magnetizations of the two thin F layers. We report direct experimental evidence for the spin-flop transition from scanning electron microscopy with polarization analysis and from spin-polarized neutron reflectometry. These results represent a first step toward experimental control of spin-triplet supercurrents.