From what I understood; the damage of a LNC/DRG comes primarily from Critical Hit Damage. In that case I would try to stack as much of my stats on Accuracy and Crit Hit Rate. For example, according to ffxivdb.com, the Allagan Cuirass of Striking has:

+29 Strength, +33 Vitality, +24 Accuracy and +34 Crit Hit Rate.

While the Darklight Cuirass has:

+20 Strength, +22 Vitality, +18 Determination and +19 Skill Speed.

As an alternative (even though it's not a cheap one), I would suggest to try and get a HQ'd Darksteel Haubergeon. It has:

+20 Strenght, +22 Vitality, +19 Skill Speed, +27 Crit Hit Rate and Materia Slots in which you can meld (for instance) Accuracy Materia.

If that suggestion would be over the top, then I would personally go for the Dragoon Myth Gear.

But, that's just a suggestion.