There is technically a more efficient way to use Infuriate and IR than to hold it for Berserk but it's so late in the expansion that I don't care enough to actually min max to this degree.

Because of the way you can front-load or back-load 2 of the FCs in your triple FC Berserk window, you can alternate between front-loading and back-loading to extend the gap between Berserks enough to justify using Infuriate off CD once every other Berserk window.

So if you front load the 2 FCs in your Berserk, that means that Infuriate will be off CD with ~27s left until Berserk is off CD. If you use Infuriate off CD, that means that when your Berserk is off CD, you'll still have ~33s left until Infuriate is read for triple FC. But, due to the 20s duration of Berserk, if you backload the 2 FCs in the next Berserk window, you technically only have ~14s until Infuriate is ready. Unless those 14s cost you a Berserk activation during the fight, it's more efficient just to Infuriate off CD between front-loaded and back-loaded triple FC Berserk windows.

But this really depends on whether or not the fight actually has a ~104s window where you can plan out each GCD so precisely and execute.

Anyways, I had originally typed up more nuanced tips but after actually checking TC's fflogs, I realized the problems might be more fundamental. Granted the parses are pretty dated but you see really fundamental issues like bad Maim and Eye up-time and a very low FC count despite high Deliverance up-time. Berserk might be important but fundamentals like getting as close to 100% Maim and Eye up-time and spending stacks with near 100% efficiency on FCs are more important.