Monaural speech separation is a crucial task in speech processing, focused on isolating single-channel audio with multiple speakers into individual streams. This problem is particularly challenging in noisy and reverberant environments where the target information becomes obscured. Cascaded multi-task learning breaks down complex tasks into simpler sub-tasks and leverages additional information for step-by-step learning, serving as an effective approach for integrating multiple objectives. However, its sequential nature often leads to over-suppression, degrading the performance of downstream modules. This article presents three main contributions. First, we propose a separation-priority pipeline to ensure that the critical separation sub-task is preserved against over-suppression. Second, to extract deeper multi-scale features, we design a consistent-stride deep encoder-decoder structure combined with depth-wise multi-receptive field fusion. Third, we advocate a training strategy that pre-trains each sub-task and applies time-varying and time-invariant weighted fine-tuning to further mitigate over-suppression. Our methods are evaluated on the open-source Libri2Mix and real-world LibriCSS datasets. Experimental results across diverse metrics demonstrate that all proposed innovations improve overall model performance.