"Do viable mature seeds always sink?"

Not always. Attached air bubbles or pieces of clinging debris can cause even good seed to float to the top. Beating vigorously with a wire whisk can free up most of the good seed, allowing it to sink. Sometimes it may be necessary to allow the seeds to soak briefly before they will sink... in which case it is extremely important to dry them quickly after cleaning. In such cases, I spread the seeds on newsprint to soak up most of the water, then place them under a fan to dry further.

You may already know this but a frequent question about saving seed is if the melon (or any veggie or fruit) you have is a heirloom or a hybrid?

Heirloom varieties are always my first choice!