Okay, so. The way I handle Hummel is vastly different than most other Dragoons I know of.

1. Why are you using Blood of the Dragon before Impulse Drive?
2. Your opener is weird as fuck. If you're gonna B4B the two Fausts, go for it, but it should look more like uh...
HT>[IR>B4B]>ID>[PS]>Dis>[BotD>LegS]>CT>[Jump]>4th>[DFD]>ID>[SSD]>Dis>[gsk]>CT>[LifeS]>4th
...ish. You can also ID the first Faust before Disembowel on the second for extra damage. Also tab-target back for the SSD to get the Disembowel buff and delay the gsk until after Disembowel applies to get double Dis buff.

Do not use SSD to close the gap to Hummel. Elusive Jump for that.
1. You can get to him before he's targetable and therefore get an immediate attack in, rather than waiting until he's targetable and then your first GCD gets delayed by SSD's animation lock.
2. Elusive is basically worthless elsewhere so why not use it?

You ended the Fausts with Full Thrust, which is super shitty, RIP dps. You also used a Phlebotomize on one of the Fausts, which is just bad practice in general. Try not to do that. It's a massive loss, especially when it precludes a gcd such as a 4th hit as the last. Lets you get +1 gsk.

Battle Litany, used when Hummel drops, is completely pointless if you're not stacking it with any buffs of your own. You're doing B4B > BL > B4B without stacking any of it. Either use it on pull for the Fausts or use it with your second B4B, not when Hummel drops. Your party should either be dropping shit on the double and then killing Hummel, or they'll be holding for Hummel. Either way, you should be doing the same thing.

If you're struggling to kill Hummel, it's because you guys aren't holding your big buffs to use on Hummel and your gear isn't good enough to cheese the fuck out of the fight, yet, so you gotta respect it more.

If you're looking to boost your personal DPS, you already seem to have figured that out with the 1633 run. I personally hold my full opener for the Hummel, with DFD+SSD+PS+Jump on the Fausts, with IR as the only buff I use there (popping it pre-pull as I run up, so it's absolutely back for Hummel). I usually do 1750+ on it, with one B4B in the fight.

...... You save Dragonfire Dive for Hummel..... for some reason?
You double-weave gsk+Jump - never do that.

Outside of that - your crit rate is super low. What are your stats? Are you over 1k Crit rate? If not, that's something to look into.