You should hold contests for the new content on who can beat it first using one of each class.
Add an achievement for doing it as well posibly with a reward.
That'll get people thinking outside the box and using all classes. (maybe lol)
Make the reward good enough and it'll probably take. Have it as a lower drop rate (not too low mind you, but similar to something you'd get out a box from a primal)
**Added**
Better still,
For primals, make it so that you can only get the weapon if you're on that class/job during the fight.
Linkshells can always start by testing with these horrid all range all blm strats, once they know and get comfortable with the fight, start changing it up and going for other weapons.
At least it'll get people having to try more strats, get all jobs being used. People won't say, "I'm sorry, you can't come, you're a MNK/DRG/PLD"
It'll also be fun because people will have to tackle the content with each new job they level, once they level it. Prolonging the life of the content.
Harder to find parties, maybe. More rewarding when you do, definitely.
Some lore for your belts:
Ifrit, The buckle was made from Ifrit's horn (attack +30)
Moogle, enchanged by the magic of moogles (Acc +30)
Garudas, Made using the feathers of garuda (eva +30 or weapon delay/casting reduction)
How about, rather then having the weapons drop like they do now, make them obtained through an achievement.
20 kills as GLA/PLD, you finish the achievement and can pick up you're sword.
50 kills going with a party set up as all classes/job, get your belt.
20 runs through the dungeon, pick a darklight peice, 100 runs for the body.
for the weapons, if they're now convertable into materia, make it every 10 kills to get you're 2nd, 3rd, 4th and so on.
At least if people knew their goals they wouldnt' have a reason to be mad at the horrid drop rates.