Presented are torque converters (TC) with hydraulic systems for converter feed and clutch control, methods for making/operating such TC assemblies, and vehicles equipped with such TC assemblies. A TC assembly includes a housing that drivingly connects to an electric motor, and an output member that drivingly connects to a multi-gear transmission. Rotatable within the TC housing are a turbine attached to the TC output member and an impeller juxtaposed with the turbine. A lockup clutch disposed inside the TC housing, between the turbine and housing, is operable to lock the housing to the output member. A disconnect clutch disposed inside the housing, between the impeller and housing, is operable to lock the housing to the impeller. A pump is attached to the TC housing and drivingly connected to the motor for feeding fluid into the housing to increase pressure within the TC chamber and activate the lockup and disconnect clutches.