Using high-resolution data sets obtained with the Hubble Space Telescope, we investigate the radial distributions of the F-type main-sequence binary fractions in the massive young Large Magellanic Cloud star clusters NGC 1805 and NGC 1818. We apply both an isochrone-fitting approach and chi^2 minimization using Monte Carlo simulations, for different mass-ratio cut-offs, q, and present a detailed comparison of the methods' performance. Both methods yield the same radial binary fraction profile for the same cluster, which therefore supports the robustness and applicability of either method to young star clusters which are as yet unaffected by the presence of multiple stellar populations. The binary fractions in these two clusters are characterized by opposite trends in their radial profiles. NGC 1805 exhibits a decreasing trend with increasing radius in the central region, followed by a slow increase to the field's binary-fraction level, while NGC 1818 shows a monotonically increasing trend. This may indicate dominance of a more complicated physical mechanism in the cluster's central region than expected a priori. Time-scale arguments imply that early dynamical mass segregation should be very efficient and, hence, likely dominates the dynamical processes in the core of NGC 1805. Meanwhile, in NGC 1818 the behavior in the core is probably dominated by disruption of soft binary systems. We speculate that this may be owing to the higher velocity dispersion in the NGC 1818 core, which creates an environment in which the efficiency of binary disruption is high compared with that in the NGC 1805 core.