A gas turbine including a working fluid flowpath extending aftward from a forward injector in a combustor. The combustor may include an inner radial wall, an outer radial wall, and, therebetween, a flow annulus, and a third radial wall formed about the outer radial wall that forms an outer flow annulus. A staged injector may intersect the flow annulus so to attain an injection point within the working fluid flowpath by which aftward and forward annulus sections are defined. Air directing structure may include an aftward intake section corresponding to the aftward annulus section and a forward intake section corresponding to the forward annulus section. The air directing structure may include a switchback coolant flowpath to direct air from the compressor discharge cavity to the staged injector. The switchback coolant flowpath may include an upstream section through the flow annulus, and a downstream section through the outer flow annulus.