According to what I see here, alot of people would like to have the Overdrive available through means outside grinding. Here's what I think: to have it available for everyone and benefit them all like so:
-Casual Players: Overdrive automatically resets every 12 hours, on a timer similar to Behest, Guildleves, Anima, and Guardian's Favor, and checkable through /clock
-Regular Players: In addition to the reset timer, it can be grinded to be used multiple times per day.
With these options above, no one would be sitting around waiting to use Overdrive. Either you're casual and it's sitting there waiting on you when you get on, or your a grinder and you're not waiting hours on end for that reset timer.

Also I believe all overdrives shouldn't be single moves, but buffs that last depending on "tier" of overdrive you're on (going by someone who posted about Overdrive having Tiers). Tier 1 is 1 minute, 2 is 1 minute 15 seconds, 3 is 1 minute 30 seconds.