By the sounds of it OP is treating oGCDs and cooldowns as one and the same. That pretty much kills every class except blm, to be honest. The exception to this is dragoon and monk. Dragoon has 11 oGCDs/cooldowns total, while Monk has 8, counting invigorate in both cases. Black Mage has 5, but their rotation is why they're difficult, if that turns you off, you're stuck with one of the melee classes, and honestly, I'd recommend dragoon for having the easiest rotation so you can learn how to manage cooldowns.

Then again, if you're not gonna escape cooldown management, why not embrace it?

Try Summoner. It's the easiest of the cooldown heavy classes to get into. It is a little weird due to the aetherflow mechanic, but despite having to track 11 cooldowns, the majority sync up every minute mark, so they're easier to manage than it seems. I'm factoring in three for garuda's pet skills, one for the aetherflow skills (there's usually only one you have to wait on each minute, fester during DWT, bane for adds during a boss outside of DWT, or Painflare on trash), and one for the aethertrail timer. It is the epitome of 15s of power followed by a period of downtime, but the down time doesn't hold your damage back. The contagion you put on your dots during tri-disaster during DWT makes them last for three quarters of every minute, and you're free to use Ruin III outside of DWT for burst or to burn MP that would otherwise go to waste due to aetherflow. Once that's mastered, the class becomes more about making decisions during downtime than it is about adhering to a strict rotation. A lower period of downtime might also warm you up to those power phases too.