Superconducting nanowire single-photon detectors (SNSPDs) in the mid-infrared (MIR) have the potential to open up numerous opportunities in fields such as exoplanet searches, direct dark matter detection, physical chemistry, and remote sensing. One challenge in pushing SNSPD sensitivity to the MIR is a decrease in the signal-to-noise ratio (SNR) of the readout signal, as the critical currents become increasingly smaller. We overcome this trade-off with a device architecture that employs impedance matching tapers and superconducting nanowire avalanche photodetectors to demonstrate increased SNR while maintaining saturated internal detection efficiency at 7.4 mu m and approaching saturation at 10.6 mu m. This work provides a platform for pushing SNSPD sensitivity to longer wavelengths while enabling the scalability to large arrays.