The utilization of hydrogen-blended hydrocarbon fuels, or even completely carbon-free fuels like pure hydrogen and ammonia, will be indispensable in the effort to reduce anthropogenic carbon dioxide emissions from heavy-duty land-based gas turbines. In order to make this energy transition, however, low emissions, low dynamics fuel-flexible gas turbine combustion systems will be required. To address some of the key technological obstacles in the development of such systems, we explore a prototype multi-element injector assembly devised to prevent flashback in extremely fast premixed hydrogen flames, paying particular attention to the impact of radial dual-fuel staging on the generation of self-induced instabilities and the formation of nitrogen oxides and carbon monoxide. In conjunction with phase-averaged OH*/CH* chemiluminescence and OH PLIF flame imaging, we carry out extensive measurements over the full range of 0 to 100% H2/CH4 fuel staging conditions, including even/uneven blends of H2/CH4 fuels between inner and outer nozzle groups, partial/complete fuel split cases, and pure H2 or CH4 fuel for all constituent flames, under a constant thermal power condition of 78 kW. Our measurements demonstrate that whereas carbon monoxide concentrations are largely unaffected by the radial fuel staging conditions except under high and pure hydrogen percentage conditions, there exists a strong correlation between total nitrogen oxides emissions and overall adiabatic flame temperature. Integrated analyses of isocontour instability maps reveal that near XH2,g = 0.50 a discontinuous mode transition takes place, where the intermediate-amplitude lower frequency oscillations associated with relatively low hydrogen concentration conditions give way to stronger, higher frequency instabilities under high hydrogen content conditions. While even-blend (non-staging) conditions are characterized by coherent oscillations of the constituent flames, the responses of clustered flames to radial fuel staging conditions are eccentric and complex, manifested as large-scale asynchronous modulations between inner- and outer-stage heterogeneous reaction zones. This observation suggests that in a multi-element injector environment spatiotemporal incoherence driven by inhomogeneous heat release can be used to neutralize self-excited pressure oscillations, by disrupting pressure-heat release coupling processes.