Alright fuck it I'm bored enough at work to bite.

Let's just assume(like you are)that no buffs are in play minus passive buffs from BLM itself and include in:
Astral fire: halves ice spells cast time at 3 stacks
Umbral ice: halves fire spells cast time at 3 stacks
First and foremost, you can get 6 Fire IVs in the standard rotation and the despair, you're assuming that people despair at 6k mana(800+800+800+1600 for the four Fire IVs + the rest for despair) which is just flat out wrong.

Alright second cast times. Okay so standard rotation vs OP: the post assumes we're coming in from a blizzard 4 and not standstill with a 2.5gcd across the board.

Fire3
Standard: 1.75s cast
OP: 3.5s cast(because OP never gets 3 umbral ice stacks with transpose)

Fire IV x2 for both: same values(5s)

Astral fire refresh
Standard: N/A triplecast + Fire IV(2.5s recast)
OP: 3.5(Fire 3)

Fire + despair
Standard: Fire IV + despair(2gcds = 5s)
OP: Fire IV x3, despair (4 gcds= 10s)

Blizzard
Standard: Blizzard 3 + Blizzard 4(1.75s+2.5s=4.25s)
OP: Transpose + 2x Blizzard 4s or paradox/xenoglossy (5s total)

Thunder:same values(2.5s)

Total time spent before repeat
Standard: 21 seconds
OP: 29.5 seconds

For every 3 OP rotations, we have 4 standards

Take P1s as the golden dummy fight since theres absolutely 0 downtime at hmm I think 8:30 is pretty generous for kill time, that's 510s. Standard as listed would be 24.28 repeats, OP would have 17.28, just toss out the decimals and go with 24 standard vs 17 OP.

Now lets put in OPs calculated potencies and multiply by the number of repeats.

Standard: 5732 x 24 = 137,568
OP: 7410 x 17 = 125,970

Look at that, OP scuffed standard rotation even loses out versus the rotation they posted. OP can't even compare both because the proposed standard has 8.5 seconds left, that's 3 full gcds the OP is just willfully cutting out.

Please go back to the drawing board and come back when you have something that works, otherwise learn the standard opener, your level 90 parties will thank you later.