Instead of an invulnerability buff on the S Rank it would be better if there would just be a message like "... is about to appear" and then you know it will spawn in 3 minutes or so.

If you want to make it even easier for all people, ask SE to remove the spawn conditions and let each hour spawn a specific S Rank so everybody knows which S Rank will spawn when. Everyone will get their kills for the achievement (what 90 % of the participants want) and can be happy.

But personally I want none of the above.