I work in midtown Manhattan and I think that the best solution to the bathroom issue is what I've seen here in most restaurants and other nightlife venues. In a small enough place, they will have unisex one-at-a-time bathrooms which have toilet and sink in them. In some very small restaurants you will find they have tiny unisex, one-at-a-time bathrooms that are small so they can fit more of them, like fitting 4 where 2 would be, and then they have one or two sinks OUTSIDE of them. This way people can go to the bathroom at their own pace and then share the sink to wash hands which takes much less time. (Added benefit is people feel shamed into always washing their hands this way, LOL)
In larger venues, like clubs and lounges, they mostly have one big "room" - it's more like an area that is set apart and when you walk in there is no door or wall, you just kind of walk around a corner. Next, you see a wall with a row of sinks and across from that you see row of stalls with toilets in them. The stalls are more enclosed - much like the aforementioned unisex one-at-a-time bathrooms in restaurants and smaller venues, so when you go in you have more privacy than in traditional stalls.
I ended up going to restrooms like this years ago and not even realizing they created a solution for a unisex restroom. in NYC, many places are cramped with limited space so they come up with creative ways to have certain features, and it felt like that's all they were doing. For all I know, that IS all some ir most? all?) of these places were doing, because this goes back YEARS. But I never felt like it was unusual or anything. I don't think any average person would notice or feel anything weird about it.
The only downside is for anyone who would need to sit because the guys would inevitably urinate on the seats.