Considering singular they has been in common use for centuries[0], changing it now would be an uphill struggle. People have used words like "ze" but they haven't caught on.
The article I linked to gives 1794 as an example of using singular they to refer to a specific person. And as it also points out, there's nothing particularly unusual about using they in the context of a specific person as well as being a plural. It is commonly accepted that "you" is now both singular and plural.
I don't think there's a better choice today than 'they' but that 1794 example doesn't show that this was a natural use back then. It was a conscious and intentional deviation from standard usage just as it is today, as was noted by the contemporary 'mansplaining' commenter and the contemporary response to him.
I can't decode what the 1794 usage was. The article describes it as "singular they", used presumably in reference to one of these three authors, but, well, it would help to see the passage in question.
English is not a dead language and so it evolves. Consider 12th century English: Ealdred arceb hine to cynge gehalgode menn guldon him gyld gislas sealdon syððan heora land bohtan.