Multi-timescale sequence modeling relies on capturing both local fast dynamics and global slow context; yet, maintaining these capabilities under the strict memory constraints common to edge devices remains an open challenge. Current State-of-the-Art models with constant memory footprints trade off long-range selectivity and high-precision modeling of fast dynamics. To overcome this trade-off within a fixed memory budget, we propose mGRADE (minimally Gated Recurrent Architecture with Delay Embedding), a hybrid-memory system that introduces inductive biases across timescales by integrating a convolution with learnable temporal spacings with a lightweight gated recurrent component. We show theoretically that the learnable spacings are equivalent to a delay embedding, enabling parameter-efficient reconstruction of partially-observed fast dynamics, while the gated recurrent component selectively maintains long-range context with minimal memory overhead. On the challenging Long-Range Arena benchmark and 35-way Google Speech Commands raw audio classification task, mGRADE reduces the memory footprint by up to a factor of 8 compared to other State-of-the-Art models, while maintaining competitive performance.