Aside from all the obvious issues, I find myself having worldbuilding problems with regards to the original society. I mean, okay, here we have a society in which one gender are warriors and one gender are slaves, with all the associated belief systems that go along with that. I concede that it is possible these people will react to a large influx of newcomers who they know used to be the opposite sex before they showed up (even if they don't know that's how the machine works, they'll find out when everyone starts yelling) by simply assigning them the roles of their current sex, with no especial confusion or uncertainty about how to treat them. I just don't think it's very likely.