You're already making up fictitious names, so how is making up fictitious sexes any different? By using non-unisex names you're implying specific sexes already. It's implausible that you would know somebody's name and details about their working conditions without knowing their sex.

Alternative solution: abbreviate all the fictitious names to single letters. This is commonly understood to mean obviously and intentionally concealed identity (e.g. "M" and "Q" from the James Bond franchise), which returns the singular "they" to traditional and unobjectionable usage.