I'll take any criticism and advice. I'm sure I'm doing plenty wrong and having a shit weapon is barely to blame.
I looked at your Butcher kill quick this morning and I see a few things you could work on.
1. During the non-Execute part of the fight it appears you're using Bladestorm outside of Colossus Smash. Instead, you should be using it on every third Colossus since the cooldowns line up perfectly. This changes once you get to Execute (and on AE fights), but is still important for the rest of the time. Similarly, you can line up Storm Bolt with every third CS as well, using it on the next CS after BS.
2. This will come with practice with the encounters and being able to look at the rest of the raid and guess how long the fight is going to last, but on Butcher you only got to use Recklessness once because you held it until 23 seconds into the fight and the fight only lasted 3:23. If you used it on pull, you would have had it up again during Execute/Timewarp. When in doubt, burn it immediately at the start and hold the second one for Execute. On Tectus through Ko'ragh the second one is a judgement call when it comes off cooldown. Look at the boss hp and decide if the fight is going to last another 3 minutes+ or not. On Imperator you can use it up to 5 times, but it's probably best to make sure that you have it for the Gorian Reaver even if that means only getting to use it 4 times total.
3. The rest is just little things... using Ravager, Storm Bolt, etc. soon after they come off cooldown. Not using Execute unless you have 60+ rage (40+ during CS). Rend uptime, especially on multi-target fights (for example on Twins, you had 44.6% uptime on Phemos and didn't Rend Pol at all). Switch to Dragon Roar instead of Storm Bolt on AE fights. Keep Sweeping Strikes up the entire time there's a flesh-eater at Brackenspore, Twins are near each other, Tectus from the time the first split happens, when Imperator summons the elemental add, etc.
(Just in case anyone who recently came back to WoW is unaware: every class has pandemic now, and DoTs will roll up to 30% of their duration when you reapply them. 18 second DoT? Refresh it with 5 seconds left on the timer and the new one is 23 seconds. You get ~100% uptime and don't waste any resources.)