My solution would be to have a modified claiming system. Before the torches come out, here's the explanation:

Once a mark spawns, it has a set radius that tracks players that come within a certain distance of it. For B rank NM's, it could be like 5 people, A ranks would track the first 15 people in range, and S ranks could track the first 30 people in range (subject to change, of course).

Once engaged - or if it engages you - those first players within range of it are given a little icon indicating that you were there first/found the NM, and if you keep the icon throughout the whole fight until the NM is defeated, you get full credit. I chose an odd number because I know some people solo or go in smaller groups with friends, but would still like full credit.
The "full credit icon" would be lost if you went out of range of the NM, in which another person could take your spot. It's a claiming system, but since people die or move out of range, others could have a chance still. This could go two ways, by allowing people WITHOUT the icon to attack (effectively discouraging them from participating OR the fight may go faster, but they get no rewards), or by LOCKING OUT the people without the icon (such as "the max capacity of participants for this Hunt has been reached").


Pros:
*It keeps the intended party size originally created for the NMs, keeping them challenging.
*It keeps parties from splitting up and covering a whole zone or multiple zones (virtually nullifying a radar), as 1 or 2 people in a full party might spot an NM, but the rest could be potentially locked out if they don't show up before others.
*It gives solo players and smaller groups a chance for full credit by working with others by keeping them alive. Imagine ........ a hunt system ENCOURAGING healing and helping out randoms.
*Full credit!

Cons:
*Known spawn points could be packed and hard to determine who was in the area first.
*Lots of people getting locked out. Though there's a chance to rejoin the fight, there's no guarantee and could lead to many missed opportunities (like minimal credit rewards aren't bad enough already XD)
*Do chocobos count?

TL;DR: This keeps the system as it was intended - for a certain number of participants to get full rewards for bringing down on-the-spot NMs. Being at the right place at the right time is a matter of time-keeping and information, not looking at a radar, so limit who gets full rewards by who was there first and keeping the battle size as was intended.

Sure there's a lot more refining to do, but this seems pretty fair and favors people that actively keep info on hunts or people who randomly find one.