Highest Health at a Given Point

I recently played a game as Sejuani finishing with 8029 health having my build consisting of 5 warmog's and the cinder-hulk enchantment. I then wondered what the highest health would be possible at any given point in the game.

There are 3 canidates for having the highest HP possible, Alistar, Nunu, and Cho'Gath (I exclude Sion, because of his unrestricted health gain). Alistar, with the highest base health at level 18 of 2347, Nunu, with his 10% bonus from consuming an elemental, and Cho'Gath, with his HP bonus from his ultimate. If they were to have 5 warmog's, cinderhulk, scaling HP runes, %HP runes, elixer of ruin, all HP masteries, and last of all, a Lulu ult at full AP, this would likely be the highest possible health. This requires me to calculate the highest health Alistar can have at one time, the highest AP Lulu can have, and add the two numbers. Here are the calculations:

Alistar

Flat Health: 7107.96

Base Health - 2347 Scaling HP Marks And Glyphs - 9.72*18 Masteries - 36 Cinderhulk - 300 5 Warmog's - 4000 Elixer of Ruin - 250

Percent Health:37%

Quints And Seals - 9% Cinderhulk - 25% Masteries - 3%

Highest Alistar Health - 9737.9052

Cho'Gath

Flat Health: 7594.96

Base Health - 1934 Scaling HP Marks And Glyphs - 9.72*18 Masteries - 36 Cinderhulk - 300 5 Warmog's - 4000 Elixer of Ruin - 250 Fully Stacked Ultimate - 900

Percent Health:37%

Quints And Seals - 9% Cinderhulk - 25% Masteries - 3%

Highest Cho'Gath Health - 10405.0952

Nunu

Flat Health: 6990.96

Base Health - 2230 Scaling HP Marks And Glyphs - 9.72*18 Masteries - 36 Cinderhulk - 300 5 Warmog's - 4000 Elixer of Ruin - 250

Percent Health:47%

Quints And Seals - 9% Cinderhulk - 25% Masteries - 3% Consume - 10%

Highest Nunu Health - 10276.7112

This leaves Cho'Gath with the highest amount of health before Lulu's ult. So next is the calculations for the most health gained from Lulu's ult.

Lulu Ult - 600 (+50% AP)

Highest AP on Lulu

Scaling AP Runes - 83 Fuly Stacked Mejais - 180 5x 120 AP Items - 600 Masteries - 22 Also Masteries - 3% Rabadons - 30%

Highest Lulu Ap: 1177.05 Most Health From Lulu Ult: 1188.525

Highest HP possible at one point (excluding Sion): at 11593.6202--

EDIT: I forgot about Cho'Gath with his ultimate's health bonus, and Nunu with his 10% health bonus from consuming an elemental (#xDarkwind).