Kawa tightness????????

I’ve just affixed my first skin on to my nagauta shamisen, (after a couple of years of procrastinating), and nobody is more surprised that the result is still playable, than myself.
However, despite stretching it to the limit of what I dare, the adventurous side of me wonders whether I should have gone further. Whilst tightening the skin it still sounded a bit muted, when tapped, though I put this down to it being wet, and would tighten further as it dried. It did so, but the skin can still be depressed a millimetre or so, therefore not as solid as I would like.
My question, (and thank you for bearing with it and reading this far), is the mild sag that… have I not tightened the skin enough; or have I over tightened it, and therefore stretched it too thin. I understand it’s difficult to specifically judge without witnessing the item, but I’d welcome observations, based on anyone’s experience.