Do “Giant’s Stance” and “Improved Natural Attack” stack as a Medium character?

Giant’s Stance states the following:

While you are in this stance, you deal damage as if you were one size larger than normal, to a maximum of Large. This benefit improves your weapon and unarmed strike damage. It does not confer any of the other benefits or drawbacks of a change in size, such as a modifier to ability scores or AC, or an improved reach.

while Improved Natural Attack states the following:

The damage for one of the creature’s natural attack forms increases by one step, as if the creature’s size had increased by one category: 1d2, 1d3, 1d4, 1d6, 1d8, 2d6, 3d6, 4d6, 6d6, 8d6, 12d6. A weapon or attack that deals 1d10 points of damage increases as follows: 1d10, 2d8, 3d8, 4d8, 6d8, 8d8, 12d8.

Giant’s Stance does have an upper limit (Large), therefore, as a Medium creature, with Improved Natural Attack making the character already Large, Giant’s Stance would have no effect. However, my thinking is that Giant’s Stance would make the character Large and after that, Improved Natural Attack would be counted as one step higher; that is, Huge.

Is this correct or do both affect the base size (that is, both convert from Medium to Large) and are therefore redundant?