Regarding being a grammar purist, it should be noted that being offended at using 'them' as a singular indefinite is a relatively recent trend.

'ze' and 've' are aesthetically unpleasing, but using them more is likely the only way they would become less so. You won't find me doing it anytime soon though.

It should be noted that until recently, 'man' was gender-neutral in English. John Stuart Mill found himself just on the cusp of that, and tried to argue for women's suffrage in England on the basis that the law referred to 'man' and so included women. (he lost). Common archaic equivalents to todays' 'man' and 'woman' are 'were' and 'wif', where 'man' meant the whole species (though commonly that only considered males).

'She' isn't that confusing, and radical feminism isn't the pernicious beast it was in the 90's, so it seems like 'she' is the best bet for a gender-neutral personal pronoun.

Personally, I prefer to invent a subject for such a thought experiment and then use the appropriate pronoun for the person's gender - which is what you did here with Theo.