strong, powerful
遒 centers on forceful strength and power, often with a sense of pressing or closing in. The idea of being strong and powerful is the core, with the pressing nuance coming from the movement radical.
遒 combines 辶 (movement) with 酋, which likely contributes the sound and the idea of pressing or strength. The exact historical development is uncertain, but the phono-semantic structure is plausible.
The movement radical 辶 surrounds 酋, which looks like a strong leader. Picture a powerful chief pressing forward, unstoppable and strong.
For シュウ, imagine a strong shoe pressing down with force: shoe -> シュウ, and the powerful movement leaves a deep impression.