> The they/them swap is the most elegant implementation I am aware of.

Far from it, it only creates confusion and injects ideologically charged "pronoun language" into the discussion. If you feel the need to make clear that yes, the person you're talking about can be a man as well as a woman - something which most people realise and the ones who don't won't anyway no matter which words you use - use something like s/he or "he or she". The first form is just as short, is not ideologically charged and does not create ambiguity.