I Fly 160 straight down, using the dash action.

Ini2, finally away from fright, uses polymorph to be a Bone Devil and heads 40ft towards the fray (or, if we want to go back to RAW with the polymorph spell, he'll go for giant eagle and fly 80ft)

Legendary action?

*lets say he’s a bone devil*

fly 40 feet toward ini15a.

Alright.

Lair Action
Ini17 (100,0,0), 2 4th expended, 1HP, polymorphed to Cloud Giant 190HP
Ini15a (100,0,40) 1 4th expended, 4 sorcery points expended, polymorphing Ini15a and Ini11, Young Blue Dragon 
Ini11 (100,40,80) away 9HP, polymorphed as Young Blue Dragon
You (100,0,80) (2/3 legendary resistances) (303 HP)
Ini2 (260,0,0) 1 4th spell expended, polymorphed as Bone Devil

lair action?

I should be at the same spot as ini15a, I’m pretty sure. 

magic swirls around me. I gain resistance to bludgeoning, slashing, and piercing damage until the next round.

You are right. My bad.

Though let's call it z-axis 45? (I know we've been loose on the occupying-same-space rules, but probably gonna be useful now that we have multiple breath attacks going)

Ini17 picks up another rock, steps 20ft to the side to get a clearer shot, and lobs it at the black dragon.

To-Hit: 21 //by the cube map, should be alright for the 20-40 to simplify to a hypotenuse of 60
Damage: 22

Not sure if you want to rule some form of cover though since we do have Ini15a right next to you and dragons are large

legendary action?

Nope.

Ini15a, with the black dragon upon him, unleashes a blast of lightning.

57 with DEX 16 for half-damage

Lair Action
Ini17 (100,20,0), 2 4th expended, 1HP, polymorphed to Cloud Giant 190HP
Ini15a (100,0,40) 1 4th expended, 4 sorcery points expended, polymorphing Ini15a and Ini11, Young Blue Dragon (needs breath recharge)
Ini11 (100,40,80) away 9HP, polymorphed as Young Blue Dragon
You (100,0,45) (2/3 legendary resistances) (303 HP)
Ini2 (260,0,0) 1 4th spell expended, polymorphed as Bone Devil

Legendary action?

Dex save:22

Oh boy, what's going on here

Alrighty. Half damage for 28. 

Ini11 swoops down 35ft, unleahses his own lightning breath, and continues down to the ground.

63 with DEX 16

Lair Action
Ini17 (100,20,0), 2 4th expended, 1HP, polymorphed to Cloud Giant 190HP
Ini15a (100,0,40) 1 4th expended, 4 sorcery points expended, polymorphing Ini15a and Ini11, Young Blue Dragon (needs breath recharge)
Ini11 (100,40,0) away 9HP, polymorphed as Young Blue Dragon (needs breath recharge)
You (100,0,45) (2/3 legendary resistances) (303 HP)
Ini2 (260,0,0) 1 4th spell expended, polymorphed as Bone Devil

Quote from Yondor_The_Fantastic >>

Oh boy, what's going on here

 1 ancient black dragon vs 6 Draconic Sorcerers, 2 of whom are dead.

I did misread polymorph so the Beast limitation isn't applied there. And so the 4 remaining are polymorphed as 2 Young Blue Dragons, 1 Cloud Giant, and 1 Bone Devil

Tail attack on ini15a

to hit: 32 damage: 14

Quote from TheFriendlyArchfey >>

Tail attack on ini15a

to hit: 32 damage: 14

 Okay.

Rolling Concentration save DC 10: 17

Dex save: 18

Same status as before, with different hitpoints (Ini11's actions still stand) your turn

Lair Action
Ini17 (100,20,0), 2 4th expended, 1HP, polymorphed to Cloud Giant 190HP
Ini15a (100,0,40) 1 4th expended, 4 sorcery points expended, polymorphing Ini15a and Ini11, 138HP Young Blue Dragon (needs breath recharge)
Ini11 (100,40,0) away 9HP, polymorphed as Young Blue Dragon (needs breath recharge)
You (100,0,45) (2/3 legendary resistances) (251 HP)
Ini2 (260,0,0) 1 4th spell expended, polymorphed as Bone Devil

EDIT: fixing your HP. Using the succeeded save from before below for 24 damage and the 28 damage I forgot to add last name from the prior breath attack

Dex save: 29

I attempt to grapple ini15a.

Strength: 23

Ini15a with contest with Athletics (STR) 18

I then fly 80 feet into the air.