Shimming is still an unavoidable, time-consuming and cumbersome burden that precedes NMR experiments, and aims to achieve a homogeneous magnetic field distribution, which is required for expressive spectroscopy measurements. This study presents multiple enhancements to AI-driven shimming. We achieve fast, quasi-iterative shimming on multiple shims simultaneously via a temporal history that combines spectra and past shim actions. Moreover, we enable efficient data collection by randomized dataset acquisition, allowing scalability to higher-order shims. Application at a low-field benchtop magnet reduces the linewidth in 87 of 100 random distortions from ∼ 4 Hz to below 1 Hz, within less than 10 NMR acquisitions. Compared to, and combined with, traditional methods, we significantly enhance both the speed and performance of shimming algorithms. In particular, AI-driven shimming needs roughly 1/3 acquisitions, and helps to avoid local minima in 96% of the cases. Our dataset and code is publicly available.