I would use "he/him" because the convention of using he/him for singular, indeterminate gender is no more difficult to understand than that "they/them" is being used as singular, indeterminate.

Ideally, I would like the people for whom this is important to use a new unambiguous word. Though this ship seems to have sailed despite there apparently being a number of possible candidates.

That aside, the author of the post to which we are referring must know the sex of his dog so why be ambiguous?