Keynote slideshow in the background
Solution 1:
The only solution I have found that's remotely workable is to augment your hardware list and use iOS to present the keynote so your computer is free to assist your teaching without interrupting the display of the keynote.
This has several disadvantages - one of which is not obvious and continually irks me (the undocumented translation bugs).
- You now need two devices - a pair of iPod touches or a combination of iPad / iPhone / iPod so that you can have one driving the display and the other as a remote to control the presentation.
- Added time to sync the presentation to iOS.
- Potentially problems driving the projector - Macs can drive more legacy video formats than iOS can with adapters. Yes, there is a $200 adapter for just about anything - but this cost is not trivial for most in education.
- iOS Keynote is not as capable as Mac Keynote and many transitions are dumbed down or not at all possible. (Worse - not all the limitations/bugs in translation are documented at the prior link)
However, if you have an iPhone, can present from another iOS device and don't mind the translation limitations - this is a fabulous and very robust presentation solution. One benefit is that you can use bluetooth or wireless and walk anywhere in the classroom while controlling the presentation.
Solution 2:
This, unfortunately, does not appear to be possible. See the question comments for more details.