Conventional means of Parkinson’s Disease (PD) screening rely on qualitative tests typically administered by trained neurologists. Tablet technologies that enable data collection during handwriting and drawing tasks may provide low-cost, portable, and instantaneous quantitative methods for high-throughput PD screening. However, past efforts to use data from tablet-based drawing processes to distinguish between PD and control populations have demonstrated only moderate classification ability. Focusing on digitized drawings of Archimedean spirals, the present study utilized data from the open-access ParkinsonHW dataset to improve existing PD drawing diagnostic pipelines. Random forest classifiers were constructed using previously documented features and highly-predictive, newly-proposed features that leverage the many unique mathematical characteristics of the Archimedean spiral. This approach yielded an AUC of 0.999 on the particular dataset we tested on, and more importantly identified interpretable features with good promise for generalization across diverse patient cohorts. It demonstrated the potency of mathematical relationships inherent to the drawing shape and the usefulness of sparse feature sets and simple models, which further enhance interpretability, in the face of limited sample size. The results of this study also inform suggestions for future drawing task design and data analytics (feature extraction, shape selection, task diversity, drawing templates, and data sharing).