I'm all for it, except the idea that urinals should go away entirely. For any place that accommodates a relatively large amount of people, they are more efficient. Just as, or even more, importantly, they keep a lot of piss off of toilet seats (I assure you a large number of guys are not lifting the seat when they piss in a public toilet and don't have good enough aim not to do so). They also conserve water.
Surely there's a way to do this and keep urinals. You could have a urinal and toilet in each stall, which some places do, solving the piss issue and conserving water, but it doesn't help with the efficiency issue if you're dealing with volumes of people. You could have a separate room or area for urinals, and then gender neutral stalls, but I guess that could still be considered exclusionary. So, I don't know, but something to think about.
As far the signage, yeah - just say "Toilet". It describes exactly what it is and is gender neutral. Simple, to the point. Even the words "restroom" and "bathroom" are kinda silly, implying that a perfectly natural bodily function is something that cannot be spoken of, as if it's something shameful.