Alright, let me begin by saying that I like the hunt system the way it is. Yes, it's frustrating to get to a monster and see the last ounce of health vanish as you receive no credit... but not everyone can win, and people can't be expected to wait forever.
That being said, allow me to throw in my $.02.
I believe when A or S rank mobs spawn, they should have a spawn immunity, of a variable time. While this won't always be relevant (if some how, a bunch of people miss a HUGE monster) generally speaking a A or S rank are found closely after their spawn time. Giving them immunity for 3-5 minutes might allow more people to get credit and alleviate some of the stress people are having.
¯\_(ツ)_/¯