Low-resolution data converters can significantly reduce the power consumption and silicon area of all-digital massive multi-user (MU) multiple-input multiple-output (MIMO) basestations. However, the existing literature almost exclusively focuses on idealistic quantization models, neglecting the inherent non-idealities present in real-world analog-to-digital converter (ADC) implementations. To overcome this limitation, we propose two affine models, one based on Bussgang's decomposition and one that maximizes the signal-to-distortion ratio (SDR), both accounting for the most prominent non-idealities in successive approximation register (SAR) ADCs. Subsequently, we utilize these models to devise low-complexity methods that mitigate SAR-ADC non-idealities in massive MU-MIMO wireless systems.