Crop type mapping at the field level is necessary for a variety of applications in agricultural monitoring and food security. As remote sensing imagery continues to increase in spatial and temporal resolution, it is becoming an increasingly powerful raw input from which to create crop type maps. Still, automated crop type mapping remains constrained by a lack of field-level crop labels for training supervised classification models. In this study, we explore the use of random forests transferred across geographic distance and time and unsupervised methods in conjunction with aggregate crop statistics for crop type mapping in the US Midwest, where we simulated the label-poor setting by depriving the models of labels in various states and years. We validated our methodology using available 30 m spatial resolution crop type labels from the US Department of Agriculture's Cropland Data Layer (CDL). Using Google Earth Engine, we computed Fourier transforms (or harmonic regressions) on the time series of Landsat Surface Reflectance and derived vegetation indices, and extracted the coefficients as features for machine learning models. We found that random forests trained on regions and years similar in growing degree days (GDD) transfer to the target region with accuracies consistently exceeding 80%. Accuracies decrease as differences in GDD expand. Unsupervised Gaussian mixture models (GMM) with class labels derived using county-level crop statistics classify crops less consistently but require no field-level labels for training. GMM achieves over 85% accuracy in states with low crop diversity (Illinois, Iowa, Indiana, Nebraska), but performs sometimes no better than random when high crop diversity interferes with clustering (North Dakota, South Dakota, Wisconsin, Michigan). Under the appropriate conditions, these methods offer options for field-resolution crop type mapping in regions around the world with few or no ground labels.