This paper enhances dysarthric and dysphonic speech recognition by fine-tuning pretrained automatic speech recognition (ASR) models on the 2023-10-05 data package of the Speech Accessibility Project (SAP), which contains the speech of 253 people with Parkinson's disease. Experiments tested methods that have been effective for Cerebral Palsy, including the use of speaker clustering and severity-dependent models, weighted fine-tuning, and multi-task learning. Best results were obtained using a multi-task learning model, in which the ASR is trained to produce an estimate of the speaker's impairment severity as an auxiliary output. The resulting word error rates are considerably improved relative to a baseline model fine-tuned using only Librispeech data, with word error rate improvements of 37.62\% and 26.97\% compared to fine-tuning on 100h and 960h of LibriSpeech data, respectively.