One method disclosed includes forming a final gate structure in a gate cavity that is laterally defined by sidewall spacers, removing a portion of the sidewall spacers to define recessed sidewall spacers, removing a portion of the final gate structure to define a recessed final gate structure and forming an etch stop on the recessed sidewall spacers and the recessed final gate structure. A transistor device disclosed herein includes a final gate structure that has an upper surface positioned at a first height level above a surface of a substrate, sidewall spacers positioned adjacent the final gate structure, the sidewall spacers having an upper surface that is positioned at a second, greater height level above the substrate, an etch stop layer formed on the upper surfaces of the sidewall spacers and the final gate structure, and a conductive contact that is conductively coupled to a contact region of the transistor.