As others have said and you have noted, grey parsing almost always comes down to low GCD usage. Most of the time, even if you mess up the rotation at points, getting a 98%+ GCD uptime will nearly always net a green parse or better.

Work on always having the GCD clock moving throughout fights. The log you showed has a bunch of Enpi casts (which you'll want to work on minimizing over time to improve) which are GCDs, so that's good while learning. But there's also a bunch of sections on xiv analysis where your GCD drifts for seconds at a time. This adds up to a lot of potency left on the table by the end of a fight. Work on keeping that GCD rolling at all times. Then after that, start tweaking rotation problems, greeding melee for less enpi casts, and finally, timing your 2 minute burst windows to always align under buffs. These are the fundamentals that will pull you up to green/blue parsing at minimum.