After trying some of the new end game contents, I manage to find some situations where Cure III is the best spell to use, examples are:
Ultima - when eating the orbs
Titan EM - Mountain Buster and phase change
Coil Turn 5 - Fireball

However, in none of the cases above, I can't see the current Overcure to have any use.

Take Freecure as an example, when I spam Cure, and Freecure pop up, there is no reason NOT to use it, even if you need to avoid over-heal, you can just wait the tank's HP to drop a bit more.

Now back to Overcure, when I spam Cure II, and Overcure pop up, really there is no reason to DO use it. It's still have less potency than Cure II, it's only cost ~10 less MP than Cure II, and when I spam Cure II usually the tank is the only one that take damage.
Then, when I really need to use it, like those situations in the beginning of the post, I never have the Overcure because I don't need to spam Cure II beforehand.

So what I'll suggest, is in addition to the MP cut, also give Cure III a HoT effect, with a duration of 15 second and potency of 50.
This way it's not really overpower (especially with the Medica II ner...change), and when I spam Cure II and Overcure pops, there is a good reason to use it. The name makes more sense as well, as now it's more like a 'Halfcure'.

Any other thoughts?