Quick reply to your aside: singular they is very grammatical and has been in use for centuries.
From Merriam-Webster: "they has been in consistent use as a singular pronoun since the late 1300s; that the development of singular they mirrors the development of the singular you from the plural you... and that regardless of what detractors say, nearly everyone uses the singular they in casual conversation and often in formal writing."[1]
From Merriam-Webster: "they has been in consistent use as a singular pronoun since the late 1300s; that the development of singular they mirrors the development of the singular you from the plural you... and that regardless of what detractors say, nearly everyone uses the singular they in casual conversation and often in formal writing."[1]
[1] https://www.merriam-webster.com/words-at-play/singular-nonbi...