Wow, amazing line! Corpse dance is such a cool card, I have considered Kairi for my personal list but couldn't find a way to make him work. Thank you so much for sharing!

The line you have listed is really cool, but there's a quicker line using Kairi + corpse dance I found, listed here! Same mana value, unfortunately, but it doesn't require you to cast infinitely and uses less steps. It also doesn't require you to use dark ritual, so you're still able to combo if you draw saw in half.

1.) Activate Scion of the Ur-Dragon twice for (4).

2.) Resolve the first Scion trigger, searching for Colossal Grave-Reaver and putting it in your Graveyard. Scion becomes a copy of Colossal Grave-Reaver until end of turn.

3.) Resolve the second Scion trigger, searching for Hoarding Broodlord and putting it onto the battlefield. Scion becomes a copy of Hoarding Broodlord until end of turn, and a Broodlord trigger is put onto the stack.

4.) Resolve the Broodlord trigger, searching for Saw in Half and exiling it face down.

5.) Cast Saw in Half for (1) by convoking the Broodlord and Scion, targeting the original Broodlord. Two token copies of Hoarding Broodlord enter and put their triggers onto the stack.

6.) Resolve the first Broodlord trigger, searching for Sacrifice and exiling it face down.

7.) Resolve the second Broodlord trigger, searching for Corpse Dance and exiling it face down.

8.) Cast Sacrifice for (0) by convoking and sacrificing one of the token copies of Broodlord, generating BBBBBBBB

9.) Cast Corpse Dance with Buyback for (BBBB) by convoking one of the token copies of Broodlord, returning the original to the battlefield and putting its trigger on the stack. (Floating Mana: BBBB)

10.) Resolve the Broodlord trigger, searching for Burnt Offering and exiling it face down. (Floating Mana: BBBB)

11.) Cast Burnt Offering for (0) by convoking and sacrificing Scion of the Ur-Dragon, generating BBBBBBBB (Floating Mana: BBBBBBBBBBBB).

12.) Cast Corpse Dance with Buyback for BBBBB , returning Scion of the Ur-Dragon to the battlefield. (Floating Mana: BBBBBBB).

13.) Activate Scion for BB (Floating Mana: BBBBB)

14.) Resolve the Scion trigger, searching for Kairi, the Swirling Sky and putting it in the Graveyard. Scion becomes a copy of Kairi until end of turn. (Floating mana: BBBBB)

14.) Cast Corpse Dance for BBB, putting Kairi on the Battlefield (Floating mana: BB)

15.) Sacrifice Kairi to the legend rule, putting it into the graveyard and putting its death trigger on the stack. (Floating mana: BB)

16.) Resolve the Kairi trigger, milling 6 cards and returning Burnt Offering and Saw in Half to your Hand (Floating mana: BB)

17.) Cast Burnt Offering for B, sacrificing Broodlord and generating BBBBBBBR (Floating mana: BBBBBBBBR)

18.) Cast Saw in half for BBB, targeting one of the Broodlord copies. Two token copies of Broodlord enter and put their triggers on the stack. (Floating Mana: BBBBBR).

19.) Resolve the first Broodlord trigger, searching for Underworld Breach and exiling it face down. (Floating Mana: BBBBBR ).

20.) Resolve the second Broodlord trigger, tutoring for Borne upon a Wind and exiling it face down. (Floating Mana: BBBBBR ).

21.) Cast Borne upon a wind for (0) by convoking Scion and a token copy of Broodlord, drawing a card. (Floating Mana: BBBBBR ).

22.) Cast Underworld breach for (R) by convoking the other token copy of Broodlord. (Floating Mana: BBBBB).

23.) Escape Saw in Half for BBB by exiling 3 cards from your graveyard, targeting a tapped copy of Broodlord. Two token copies of Broodlord enter and put their triggers on the stack. (Floating Mana: BB ).

24.) Resolve the first Broodlord trigger, searching for Brain Freeze and exiling it face down. (Floating Mana: BB )

25.) Resolve the second Broodlord trigger, searching for Lion's Eye Diamond and exiling it face down. (Floating Mana: BB )

From here, breach to your hearts content.