A gas turbine engine having a turbine that includes a stator blade and a rotor blade having a seal formed in a trench cavity defined therebetween. The seal may include: a stator overhang extending from the stator blade toward the rotor blade so to include an overhang topside, and, opposite the overhang topside, an overhang underside; a rotor outboard face extending radially inboard from a platform edge, the rotor outboard face opposing at least a portion of the overhang face across the axial gap of the trench cavity; an axial projection extending from the rotor outboard face toward the stator blade so to axially overlap with the stator overhang; and an interior cooling channel extending through the stator overhang to a port formed through the overhang underside. The port may be configured to direct a coolant expelled therefrom toward the axial projection.