As it stands, that is the problem with current white mage to be honest. In terms of identity, I feel it should be a mirror to BLM in in the sense that its identity is to be the healer with long cast times and powerful gcds as a consequence. Its output per gcd is better rewarded and/or less punishing than it would be on other healers. To take it to the same extreme as blm, you could outright make it the turret healer that spends most of its time standing still, with a few tools to help with its mobilty. Or perhaps you could set it up in such a way that its a matter of balancing healing and dps in similar fashion to redmage with its black and white mana. For example;
Cure, Cure II, Cure III, Medica, Medica II:
Additional effect: Grants two Touch of Earth or removes one Touch of Light, to a maximum of 6.
Touch of Earth effect: Increases damage dealt by certain spells by 50%.
Glare III, Dia, Holy, Afflatus Misery:
Additional effect: Grants two Touch of Light or removes one Touch of Earth, to a maximum of 6.
Touch of Light effect: Increases healing magic potency of certain spells by 20%.
What this would mean is that, assuming you used 3 gcds to heal, you would then get 6 gcd's of bonus damage on glare, dia, holy or afflatus misery to gradually compensate the damage you would have lost. In terms of minmaxing for end content, you could go so far as to make sure you get at least one use of Touch of Earth on afflatus misery or dia (assuming it applies to more than just the initial damage) for the extra dps overall, which in turn also makes the lilies a net positive rather than just neutral. Alternatively rather than stacks you could simply make it some kind of linear gauge that just gradually increases to a fixed amount, and you spend portions at a time, like sch's faerie gauge. In either case, you are compensating for the dps otherwise lost because of gcd healing, without making it a forced aspect of the class' rotation or functionality, except for the singular case of using it to empower Aff. Misery.
Another idea is that you could focus more on the lilies instead, and give white mage a soft rotation as mentioned here.
As for its gimmick, I would assume that would be its lilies, unless you imagined something else?