Yeah, whenever I see a fight for the first time, I fall back into 2.0 mode for pretty much the entire fight. Mainly because even when I use Enochian, I get locked out of it constantly since I have no idea when the jumps, immunities and the like come up. That's part of learning though, and my dps is down by 30-50% so I don't think it's something to recommend doing past that learning stage.
Going back to the original topic of "fixes" for the class:
I think maybe the order in which you get your new skills could/should be different. The way it is now, you get lots of supportive abilities first which are kind of useless by itsself and only when you hit 60, they give you access to your new rotation and throw you into the new lvl 60 content right away without any time to get used to it (yes, yes, you can train your new rotation on a dummy but it will not teach you how to move with it and your first encounters will be incredibly stressful. Even I kept on thinking "omg I suck so much at this new BLM, I think I'll have to quit this class, this is so stressful, nobody is gonna take me into raids like this". It got better)
So I suggest to change it up a bit:
First you get Enochian. At lvl 52, it's just a nice, 30 seconds buff to your dmg, just like Raging Strikes, not much to think about here.
At 54, you get Fire4. You'll get used to it's casttime and relation to Astral Fire, and seeing the destruction you cause in those 30 seconds of Enochian uptime will make you wish you could keep on doing that :3
At 56, you get Ice 4, so now you can do the general 3.0 rotation. Still lots of level dungeon runs ahead to get used to it, and since you already know how the management of Fire 4 with the Astral Fire timer works, getting Ice 4 is welcome to extend the time you can throw giant fireballs at your target.
At 58 and 60 you get Augmentation and Ley Lines, skills that make it easier to work with the new rotation, but that are in no way needed. And since you had to do without them before, it will actually feel easier once you hit 60, not harder
Look at BRD, they get their gameplay-changing skill (WM) right at the start, so they can get used to the restriction of movement right away, and as they level up, they get the skills that make WM worth having as well as skills that just make things easier a bit.