A rotor blade for use in combustion turbine engine. The rotor blade may include: an airfoil assembled from two radially stacked non-integral sections in which a body section resides inboard of a cap section; an outboard tip of the airfoil that is enclosed by a tip plate having a tip rail; and a cooling configuration that includes cooling channels for directing a coolant through the rotor blade. Each of the cooling channels may include segments, in which: a supply segment extends radially through the airfoil, the supply segment being radially defined between a floor and ceiling; a rail segment extends through an interior of the tip rail; and a connecting segment extends between the supply segment and rail segment. For each of the one or more cooling channels, the ceiling of the supply segment may be defined within the cap section of the airfoil.