I think that the most sensible thing to do is to simply refer to other people as Them, Their or They if you're unsure about their preferred pronoun. Realistically, no people are not asking everyone what their preferred pronoun is and while it could be nice it would ultimately be better to refer to people using the neutral pronoun that is socially acceptable rather than making up something crazy that isn't even a word. No one blinks an eye if you say the elderly person (gender unspecified) dropped their hat. If you say they dropped gir/ze/ish hat then, well, it's just kind of unnatural and doesn't really prove anything that saying their won't prove.
I haven't gotten blank stares either - when I was first beginning transition I had to correct people when they called me by the wrong pronoun, but that time passed and now I don't have to deal with it.