We present experimental and theoretical studies of single-molecule conductance through nonplanar fullerocurcuminoid molecular dyads in ambient conditions using the mechanically controllable break junction technique. We show that molecular dyads with bare fullerenes form configurations with conductance features related to different transport channels within the molecules, as identified with filtering and clustering methods. The primary channel corresponds to charge transport through the methylthio-terminated backbone. Additional low-conductance channels involve one backbone side and the fullerene. In fullerenes with four additional equatorial diethyl malonate groups attached to them, the latter transport pathway is blocked. Density functional theory calculations corroborate the experimental observations. In combination with nonequilibrium green functions, the conductance values of the fullerocurcuminoid backbones are found to be similar to those of a planar curcuminoid molecule without a fullerene attached. In the nonplanar fullerocurcuminoid systems, the highest-conductance peak occurs partly through space, compensating for the charge delocalization loss present in the curcuminoid system.