One of the major obstacles for designing solutions against the imminent climate crisis is the scarcity of high spatio-temporal resolution model projections for variables such as precipitation. This kind of information is crucial for impact studies in fields like hydrology, agronomy, ecology, and risk management. The currently highest spatial resolution datasets on a daily scale for projected conditions fail to represent complex local variability. We used deep-learning-based statistical downscaling methods to obtain daily 1 km resolution gridded data for precipitation in the Eastern Ore Mountains in Saxony, Germany. We built upon the well-established climate4R framework, while adding modifications to its base-code, and introducing skip connections-based deep learning architectures, such as U-Net and U-Net++. We also aimed to address the known general reproducibility issues by creating a containerized environment with multi-GPU (graphic processing unit) and TensorFlow's deterministic operations support. The perfect prognosis approach was applied using the ERA5 reanalysis and the ReKIS (Regional Climate Information System for Saxony, Saxony-Anhalt, and Thuringia) dataset. The results were validated with the robust VALUE framework. The introduced architectures show a clear performance improvement when compared to previous statistical downscaling benchmarks. The best performing architecture had a small increase in total number of parameters, in contrast with the benchmark, and a training time of less than 6 min with one NVIDIA A-100 GPU. Characteristics of the deep learning models configurations that promote their suitability for this specific task were identified, tested, and argued. Full model repeatability was achieved employing the same physical GPU, which is key to build trust in deep learning applications. The EURO-CORDEX dataset is meant to be coupled with the trained models to generate a high-resolution ensemble, which can serve as input to multi-purpose impact models.