Is it possible to have a campaign covering lots of countries / lots of different time zones, and to have ads showing only during particular times of day as per those time zones -- for example between 9a and 5p for each time zone?
Seems that this is possible:
Ad Scheduling (also known as "day parting") lets you tell Google exactly when you want your ads to run, and more importantly, when you do not want them to run. In addition, more advanced users can automatically modify their bids based on time-of-day and day-of-week cycles in campaign performance.
Ad Scheduling can help you with improving ROI for your display campaigns by ensuring that your ads show at times where it performs the best. For example, if you notice that you are getting the most conversions from Monday to Friday and nothing on Saturday and Sunday, you can schedule your ads to appear only during those times so that you are maximizing your ad's performance with your given budget.
It also says "You can set an ad schedule for particular hours of the day, or specific days of the week", so this looks like what you want. Still might be a fair bit of work to set up, of course...