But doing both at once seems unmotivated. If I'm willing to ignore English grammatical conventions enough to make up new pronouns altogether, I don't see on what grounds I can object to someone else ignoring subject/object matching rules.

I don't consider the creation of words to fall under the auspices of grammar. That happens in English and other languages all the time, because new or different concepts frequently need to be expressed in ways that are unavailable in the current state of the language. Using new words promotes clarity, in the long term, but misusing current words does the opposite.