A hydrokinetic torque coupling device features an impeller including an impeller shell and impeller blades, and a turbine-piston including a turbine-piston shell and turbine blades. The turbine-piston is movable axially toward and away from the impeller shell to position the torque converter (or a hydrokinetic torque coupling device containing the torque converter) into and out of lockup mode. The impeller shell comprises a toroidal impeller shell portion that terminates at a first distal end clutch surface. The turbine-piston shell comprises a toroidal turbine-piston shell portion and a folded-over portion folded over onto the toroidal turbine-piston shell portion so as to engage the toroidal turbine-piston shell portion of the turbine-piston shell. The turbine-piston shell terminates at a second distal end clutch surface defined by the toroidal turbine-piston shell portion and the folded-over portion so that the second distal end clutch surface faces the first distal end clutch surface.