Honestly, this is how I thought it would be. Each week you would get an Elite Mark in your Journal as a quest, you form a party, you go to the area designated, initiate the quest, and kill it. Only people in your current party can attack your mark, so you don't have to worry about anyone claiming it before you.
I know people wouldn't be able to farm endless Allied Seals this way, since the game would only technically allow you to spawn one Elite Mark per week, but maybe they could have it so that if you complete the quest for five Regular Marks, you would gain access to another quest for an Elite Mark? As it stands, very few people [if any] do the quests for Standard Marks, since their payout is so low and likely isn't worth their time traveling the distances to kill it.
This is what I thought it was going to be; like FFXII. You have to accept the bill from the Hunt Board, go to the required location and then your mob will be instanced in, like a leve, and if you wanted people to help you could do that. Not roaming monsters that can be zerged by half the server in a minute, or being able to exploit with a program.
It wasn;t until after I accepted the bill from the hunt board and talked with others that I realized that taking a bill simply means I'll get a bonus should I find the mob/actually be able to get a hit on it before I'm swarmed and my computer blows up.
Then those would be capped for the week; one elite bill a week to find an elite mob and then five for rank B and A. The way it worked in FFXII was perfect. You accept the bills for the elite marks, and then you have those 80 random rare monsters that will spawn under certain conditions.