I think you're misunderstanding:

1. who "we" are; and
2. what "we" are trying to achieve.

You wrote:

I take it that Stack Exchange Inc. wants (at least) the following things:

• To have a welcoming environment where no one feels as if they're fair game for rude and marginalizing language.
• Not to do things that result in a large fraction of the community, or of particular parts of the community (e.g., moderators), feeling alienated.

It's actually the opposite. "We" are StackExchange Inc. And what "we" are doing is creating an unwelcome environment for moderators and users who keep an open mind and a critical attitude regarding the company's behavior and policies, and it seems (and is even hinted) that intent is making such people leave.

The whole gendered-pronoun business, itself, is being used as a Red Herring for that purpose. Statistically, it seems to barely ever come up (other than in the "don't assume my gender" variety). So really, don't sweat it, the matter is covered well enough by a general "be nice" principle. No need for a CoC for that.

I think you're misunderstanding:

1. who "we" are; and
2. what "we" are trying to achieve.

You wrote:

I take it that Stack Exchange Inc. wants (at least) the following things:

• To have a welcoming environment where no one feels as if they're fair game for rude and marginalizing language.
• Not to do things that result in a large fraction of the community, or of particular parts of the community (e.g., moderators), feeling alienated.

It's actually the opposite. "We" are StackExchange Inc. And what "we" are doing is creating an unwelcome environment for moderators and users who keep an open mind and a critical attitude regarding the company's behavior and policies, and it seems (and is even hinted) that the intent is making such people leave.

The whole gendered-pronoun business is being used as a Red Herring for that purpose. Statistically, it seems to barely ever come up (other than in the "don't assume my gender" variety). So really, don't sweat it, the matter is covered well enough by a general "be nice" principle. No need for a CoC for that.