Predicting the unprecedented, nonlinear nature of COVID-19 presents a significant public health challenge. Recent advances in deep learning, such as Graph Neural Networks, Recurrent Neural Networks (RNNs), and Transformers, have enhanced predictions by modeling regional interactions, managing autoregressive time series, and identifying long-term dependencies. However, prior works often feature shallow integration of these models, leading to simplistic graph embeddings and inadequate analysis across different graph types. Additionally, excessive reliance on historical COVID-19 data limits the potential of utilizing time-lagged data, such as intervention policy information. To address these challenges, we introduce ReGraFT, a novel Sequence-to-Sequence model designed for robust long-term forecasting of COVID-19. ReGraFT integrates Multigraph-Gated Recurrent Units (MGRUs) with adaptive graphs, leveraging data from individual states, including infection rates, policy changes, and interstate travel. First, ReGraFT employs adaptive MGRU cells within an RNN framework to capture inter-regional dependencies, dynamically modeling complex transmission dynamics. Second, the model features a Self-Normalizing Priming layer using SELUs to enhance stability and accuracy across short, medium, and long-term forecasts. Lastly, ReGraFT systematically compares and integrates various graph types derived from fully connected layers, pooling, and attention-based mechanisms to provide a nuanced representation of inter-regional relationships. By incorporating lagged COVID-19 policy data, ReGraFT refines forecasts, demonstrating RMSE reductions of 2.39-35.92% compared to state-of-the-art models. This work provides accurate long-term predictions, aiding in better public health decisions. Our code is available at https://github.com/mfriendly/ReGraFT.