A rotor blade (16) for a turbine of a gas turbine that includes an airfoil (25). The airfoil may have a leading edge, a trailing edge, an outboard tip, and an inboard end where the airfoil attaches to a root configured to couple the turbine blade to a rotor disc. The airfoil (25) may include a tip shroud (55) at an outboard tip. The rotor blade may have a cooling configuration that includes: elongated cooling channels (33) for receiving and directing a coolant through the airfoil (25); and branching passages (75) formed through the tip shroud (55), each of which elongates between a connection with one of the cooling channels (33) and an outlet port (37) formed on a surface of the tip shroud (55). The branching passages (75) may have a canted orientation relative the outboard surface of the tip shroud (55).