We construct new models of “curved” SU(4|1) supersymmetric mechanics based on two versions of the off-shell multiplet (8, 8, 0) which are “mirror” to each other. The worldline realizations of the supergroup SU(4|1) are treated as a deformation of flat N= 8 , d = 1 supersymmetry. Using SU(4|1) chiral superfields, we derive invariant actions for the first-type (8, 8, 0) multiplet, which parametrizes special Kähler manifolds. Since we are not aware of a manifestly SU(4|1) covariant superfield formalism for the second-type (8, 8, 0) multiplet, we perform a general construction of SU(4|1) invariant actions for both multiplet types in terms of SU(2|1) superfields. An important class of such actions enjoys superconformal OSp(8|2) invariance. We also build off-shell actions for the SU(4|1) multiplets (6, 8, 2) and (7, 8, 1) through appropriate substitutions for the component fields in the (8, 8, 0) actions. The (6, 8, 2) actions are shown to respect superconformal SU(4|1, 1) invariance.