My thoughts:

Make the system set up where word is sent to the cities and a nearby NPC to where the HNM spawns. There will be criers in town shouting that a monster was spotted at X location. You enlist with the NPC and go to fight it.

The HNM would need to be strong enough that a many groups of people would be required to kill it. When the NM is defeated, the nations defenders or maybe the GC for that region take control of the site.

After a period of time, you get a parcel in the mail, stating that they found a stash of loot on the monster or in its lair, and here's your cut. Items, gil, gear, whatever the HNM stashes, has a chance of dropping to you provided you contributed to the kill. This could be set to a threshold, where only the most active people have a chance at the good loot, so someone who tags the mob with one ability and goes AFK will get little in reward.

This would keep the players happy, as everyone can contribute, and a large number are needed to contribute to make it happen. It would prevent groups from monopolizing the HNMs, which was a huge issue in XI. If they want, they can still keep the drop rates on the best gear at a low chance, to make it worthwhile to keep fighting them, which is why the HNM system works in the first place.