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DISCLAIMER: please, before you read "Tag" & think "Claim", please read the entirety of the post & realize this' an INCLUSIVE solution that fits well into the current cooperative nature of Hunting & not an exclusive one.
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Give us all an ability, "Tag Mark".
The finder comes upon the Mark, they tag it.
Then either 1 of 2 things happens, depending on SE's preference.
1) the creature becomes invulnerable for 2 minutes while your allies gather.
2) the creature becomes invulnerable for 1 minutes, your allies are offered a teleport to your location* (1 minute to compensate for slow load-times).
What Tag Mark does is either double-triple the contribution score of your party against the mark* (after the invulnerability has worn off).
After the invincibility expires, the Mark is 'Tag-Immune' for like 4-5 more minutes.
Tag-Immunity prevents the Mark from being retagged by somebody else... this prevents abuse cases of people Tagging & leaving, etc. This also flags the system for your party's contribution bonus.
Additionally, once the invincibility wears off, anyone can then attack/pull the mob. 1-2 minutes untouchable is a sufficient waiting time & people can still do as we've done on Coeurl & try to enforce some kind of 'house rule'/etiquette/pull-time.
Additions which compliment this idea well (practically required to solve Hunting's Issues):
1) Prevent mob-reset. Rather drop the resettor off the enmity list & have the mob bump up enmity target # 2. In this system, healthy mob resetting (counteracting troll pullers) won't be a necessity, and unhealthy mob resetting will be eliminated.
2) Prioritize mark rendering. We all know the plethora of issues with mobs phasing out of existence, SE this' a must, no argument there.
3) Alter contribution formulae. This' my personal throw-in & not necessarily required. Though I think it's cheesy & lame the way the current system rewards gross overhealing spam. Best way to full-credit? Prep Medica II, tap the mob once with Aero I, then Medica spam for days. Solution? Significantly increase the contribution score from damage-dealing & (maybe) decrease the contribution score from overhealing. With the former, at least damage-comps can earn their deserved credit rather than not standing a chance most of the time.
*Members must be in-party at the time of the Tag to receive this bonus.
Done & done. Hunts fixed.
P.S. S Ranks can not be Tagged.