I'm assuming that rotation includes your opener? If so, you need to use Perfect Balance. Try this:
(Form Shift to Coeurl)
Demolish
[Perfect Balance]
Snap Punch
[Potion, if you're gonna use it, or Diversion if you're worried about tank threat]
Snap Punch
[Riddle of Fire]
Dragon kick
[Internal Release ->Forbidden Chakra]
Twin Snakes
[Elixir Field -> Brotherhood]
Snap Punch
[Howling Fist -> Steel Peak]
*From here on, do the normal thing with keeping up DKick / Twin Snakes and Demolish*
(There's other openers out there that are slightly different, like intentionally clipping Demolish early or postponing your oGCDs even further. They're all kind of a wash overall but they're all better than what you're doing now.)

Pretty much you wanna maximize your oGCD usage during Riddle of Fire, since they're not penalized with the 15% GCD penalty but do get the 30% damage boost.

Looking at an Alte log from 4 days ago, you also seem to be letting twin snakes and dragon kick fall off. Twin Snakes only had a 67% uptime, and Dragon Kick about 66% -- they should be about 98% or above in a fight like that. As a general rule, your opo-opo stance and raptor stance abilities should flip between dragon kick/twin snakes and bootshine/true strike every other combo. Demolish should be used every third combo, otherwise snap punch.

Ex:
DK, Twin, Demolish.
BS, True, Snap.
DK, Twin, Snap.
BS, True, Demolish.
DK, Twin, Snap.
BS, True, Snap.
Repeat!

You lost Greased Lightning three times fighting Alte -- you should ensure that you don't ever let it fall off. Eeeeever. Greased lightning is life. Use Riddle of Earth if you really need to refresh it for mechanics (like the thunder spread), but there's nothing during the Alte fight that requires that -- at no point are you off the boss long enough to lose GL3 naturally.

Riddle of Fire was only used 3 times in that fight despite it being almost 8 minutes long. In a fight like that it should be cast at least five, closer to 6 times. Pretty much after your opener, use it on cooldown, alongside Brotherhood (the bonus chakras from brohood mean more forbidden chakras, and a forbidden chakra during riddle of fire is extremely potent.)

Actually looking at it, none of your off-GCD skills are utilized as often as they should be. You only used Elixir Field 11 times during the fight -- it should be hit on cooldown, same with fire tackle, steel peak, and howling fist. You only used Fire Tackle twice -- it's free damage, and unless the fight requires you to use it for movement (none of the current endgame fights do) you should be mashing that thing on cooldown.

Even further, it seems there's times where you're not pressing your combo on cooldown -- practice your combo on a dummy until you are constantly flowing. Don't hesitate, punch the damned dragon!

Lastly, you said you know positionals and while it's tricky to see if you miss any from logs, I can see Bootshine only had a 69% crit rate -- Bootshine should have *very few* uses in a fight like that where it's not guaranteed to crit.

tl;dr, practice a more efficient opener, make sure your buffs and debuffs don't fall off, and make sure you're using all of your off-GCD skills as they come off cooldown. Be sure to work on your positionals too. Push buttons harder! Faster!