A torque converter includes an impeller, a turbine-piston hydrodynamically drivable by the impeller, a stator, and an annular lockup resistance member. The impeller includes an impeller shell. The turbine-piston includes a turbine-piston shell. The turbine-piston shell includes a turbine-piston flange having a first flange surface facing an engagement surface of the impeller shell. The turbine-piston is movable axially toward and away from the engagement surface to position the torque converter into and out of a lockup mode in which the turbine-piston flange is mechanically locked to the impeller shell. The annular lockup resistance member is in the form of an annular elastomeric sandwich washer coaxially aligned with the rotational axis and including turbine-side and stator-side members, and an elastomeric inner member sandwiched between the turbine-side and stator-side members.