Well, one of those problems has been eliminated with this new plugin for Open Office. It only works with Open Office 3 or above (I'm using 3.0.1). You'll also need to download the extension from the project page which you can find here:
Go to Tools -> Package Manager and browse to the .oxt file you downloaded from the site, and restart Impress - hopefully everything should just work! The settings are hidden in the "Slideshow Settings" screen, look right at the bottom. And with luck, you'll see your slides on your second screen as usual, and something like this on your main screen:
All I need to do now is figure out why I sometimes have issues with xrandr and projectors, and I'll be ready to go!