One illustrative device disclosed herein includes, among other things, a stepped conductive source/drain structure with a first recess defined therein and a stepped final gate structure with a second recess defined therein, wherein, when viewed from above, the second recess is axially and laterally offset from the first recess. In this example, the device also includes a layer of insulating material positioned above the stepped conductive source/drain structure and the stepped final gate structure, a conductive gate (CB) contact that is conductively coupled to the stepped final gate structure and a conductive source/drain (CA) contact that is conductively coupled to the stepped conductive source/drain structure.