A MHz-rate mid-infrared laser absorption sensing strategy has been developed to simultaneously measure the intra-cycle variation of carbon monoxide (CO), carbon dioxide (CO$_2$), water (H$_2$O), pressure, and temperature in the chamber of rotating detonating rocket engines (RDREs). The beams of two quantum cascade lasers (QCL) and one interband cascade laser (ICL) were multiplexed to target rovibrational transitions in the fundamental bands of CO and H$_2$O (at 5 µm) and CO$_2$ (at 4.2 µm). Extended trapezoidal injection current modulation via bias-tee circuitry provided sufficient spectral range to fully resolve collisionally broadened spectral transitions with a 1-µs time resolution. The three laser beams are coupled into a single optical fiber for light delivery through a sapphire window and into the annulus of a gaseous methane-oxygen rotating detonation rocket engine (RDRE) at the Air Force Research Lab in Edwards, CA. The light was retro-reflected from the annulus centerbody and spectrally demultiplexed onto two photovoltaic (PV) detectors. Quantitative, three-species concentration measurements, along with temperature and pressure, were inferred from the spectrally-resolved signals at 1 MHz over a range of post-detonation, in-chamber conditions, 1500–3000 K and 1–5 atm at targeted propellant mass flow rates ranging from 0.09–0.36 kg/s. The integrated five-parameter measurement scheme captures approximately 80% of the total combustion gas composition and fully characterizes the thermodynamic state at detonation-relevant time-scales, offering broad applicability to high-speed combustion flows.