Bed-based pressure-sensitive mats (PSMs) offer a non-intrusive way of monitoring patients during sleep. We focus on four-way sleep position classification using data collected from a PSM placed under a mattress in a sleep clinic. Sleep positions can affect sleep quality and the prevalence of sleep disorders, such as apnea. Measurements were performed on patients with suspected sleep disorders referred for assessments at a sleep clinic. Training deep learning models can be challenging in clinical settings due to the need for large amounts of labeled data. To overcome the shortage of labeled training data, we utilize transfer learning to adapt pre-trained deep learning models to accurately estimate sleep positions from a low-resolution PSM dataset collected in a polysomnography sleep lab. Our approach leverages Vision Transformer models pre-trained on ImageNet using masked autoencoding (ViTMAE) and a pre-trained model for human pose estimation (ViTPose). These approaches outperform previous work from PSM-based sleep pose classification using deep learning (TCN) as well as traditional machine learning models (SVM, XGBoost, Random Forest) that use engineered features. We evaluate the performance of sleep position classification from 112 nights of patient recordings and validate it on a higher resolution 13-patient dataset. Despite the challenges of differentiating between sleep positions from low-resolution PSM data, our approach shows promise for real-world deployment in clinical settings