lander, I too have often wished for a nongendered set of pronouns. I don't like to use the plural pronouns as substitutes when they are being used to signify a singular; I don't like the awkwardness of the he-or-she construction; I don't like the default of the singular masculine pronoun when the noun might be feminine, although I use it for lack of an alternative.

I have mentally substituted "che" for "he or she". It seems like one could similarly tweek him-or-her, his-or-hers. Herm and hez?

Good luck.