One of the benefits of 36-spoke wheels is that -- when you DO break a spoke -- you usually don't notice. A 32H wheel will probably wobble and rub your brakes, a 36H usually doesn't.
Of course it's better to replace a broken spoke. But if the situation calls for it, I'd keep going on 36H wheels. Depends mostly on the terrain (wouldn't do it on bone-jarring paths), and the weight on the rear wheel (maybe send some of your gear ahead?). If it gets to the point where you have cascading broken spokes, it's time to catch the next bus. Or risk your rim. But chances are you won't have that problem. I bet once you get riding, you'll forget to "baby" it, and all will be well till Chengdu.
But first try MichaelW's tip. It'll work and give you piece of mind.
When you get to town, get a handful of replacement spokes, the tool, and the knowledge to change them. That should give you 95% confidence to get through anything. Or if you've got another 2 years to go, it might be time to rebuild the wheel. It's possible your weakest spoke just gave out, but in general they wear about evenly (on a well-tensioned wheel). This isn't alarmist, just saying it would give you the last 5% of confidence.
Sounds like a fantastic ride..... and a great website. Buena suerte!
-- Mark