Individuals with speech disabilities rely on everyday technologies powered by Automatic Speech Recognition (ASR) systems, yet these systems consistently fail them–producing significantly higher error rates that undermine the usefulness of voice assistants, hands-free devices, and machine translation pipelines. We conduct a multi-stage evaluation of speech impairment effects in cascaded speech-to-text translation, examining two distinct conditions: real dysarthric speech and simulated rhotacism. For dysarthria, we quantify ASR error rates. For rhotacism, we quantify error rates from a minimal-pair text substitution. We then analyze how impairment-induced errors propagate through downstream machine translation across three language directions (English to Spanish, Ukrainian, Khmer), and propose a training-free LLM-based post-correction methodology as an accessible intervention. We find that larger LLMs (70B parameters or more) consistently improve downstream translation quality even when surface-level corrections made by those LLMs remain modest, while smaller models lack the capacity to do so reliably. These results reveal a promising but scale-dependent path toward more equitable speech technology for users with atypical speech.