A gas turbine that includes 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. 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 that corresponds to the aftward annulus section and a forward intake section that corresponds to the forward annulus section. The air directing structure may be configured to: direct air entering through the aftward intake section through the aftward annulus section in a forward direction to the staged injector; and direct air entering through the forward intake section through the forward annulus section in a forward direction to the forward injector.