There has to be more than just one international school in Beijing and, as you correctly surmised from the Guide, international schools and China branches of Western universities are the only route you should be taking.
I know it will be tempting but, please, do not even consider teaching "oral English" in China as a stopgap measure until something more appropriate comes along. Doing so will significantly decrease your chances of ever doing anything else in China.
I would suggest you just keep plugging away at the various international schools in China, even if that means teaching in Shanghai or Guangzhou. It won't be an ideal situation, of course, but at least you will both be in the same country. There are millions of happily married Chinese couples who live and work in different provinces so this is not a concept that will be foreign to your girlfriend (although it is to us).
Best of luck with this. Let us know where you finally land.