Is it possible to run RoboVM under Windows or do I need to have MacOS available somewhere?
If not, is there an alternative (that also creates as-close-to-native-as-possible output) that does run under Windows?
There was a project to compile RoboVM on Windows but its goal was not to create iOS apps. Even if you could do that you would not be able to use the native iOS simulator which RoboVM relies on, it also needs xcode installed so I'm guessing that won't work.
Codename One allows using Windows/Linux with the cloud build although I'm not sure if it satisfies your close to native concept. The apps are native and have access to native functionality/Objective-C but most of the UI is rendered on top of Open GL.