I love the concept of HNM's as they existed in FFXI, and would love to see them implemented to XIV. However, when FFXI was at its peak the only people claiming HNM's were Linkshells with NASA bot. NASA bot was a program that sold for about $1000 USD. Groups of players within Linkshells would pool their money together to buy it, and the ones who put up the money for it would usually have precedence over those who didn't in regards to drops. This made the system unbalanced.
So what's the solution? Well, it's possible to follow in the steps FFXI similar to sky or sea, but that presents it's own problem with trying to claim the NM's that drop the pop items. Another option is to emulate the ZNM system, and it looks a little bit like that's direction that XIV is taking. The problem with ZNMs in XI was in loosing a fight, exorbitant amount of time and effort were also lost. Not to mention climbing the tiers through ZNMs just to get the tiers that actually had decent loot was very boring. It seems like XIV's solution to that problem is to make the fights underwhelmingly easy, and as such to have undesirable rewards. Don't try to bother figuring out what the development team is thinking. They don't play MMOs they just attempt to make them lol.
While all of those options have a chance at half-hazardly working. I think the best would solution would be based on a simple random number generator. For example:
HNM's would have spawn windows identical to the ones in FFXI. Any time a HNM is killed registration for the next spawn window would start. Any Linkshells or "Free Companies" as it were, would then be eligible for registration by having the leader (or sub leaders) speak with a HNM registration NPC in any one of the main cities.
After the registration is complete, everyone could go about what ever activities they wished even during the spawn window of the HNM. The spawn window could be two hours for example, during which time anyone wishing to participate should remain online. When the HNM pops the leaders of all the free companies that registered will receive a message notifying them of it, and also who the winning party is. The winning party will have 15 minutes(maybe more or less?) to assemble their alliance with the at least the minimum members, and gather at the spawning location.
If the winning party wipes the privilege would be given to the winner of another random number generation done by the system. Then the system would repeat. The winners of the lot will be ineligible for registration for 48 hours, with the exception of the event in which 0 free companies register for the fight. Simple and flawless in my opinion.