One illustrative integrated circuit (IC) product disclosed herein includes a first conductive source/drain contact structure of a first transistor with an insulating source/drain cap positioned above at least a portion of an upper surface of the first conductive source/drain contact structure and a gate-to-source/drain (GSD) contact structure that is conductively coupled to the first conductive source/drain contact structure and a first gate structure of a second transistor. In this example, the product also includes a gate contact structure that is conductively coupled to a second gate structure of a third transistor, wherein an upper surface of each of the GSD contact structure and the gate contact structure is positioned at a first level that is at a level that is above a level of an upper surface of the insulating source/drain cap.