Thanks for the responses everyone. I can confirm that moving an element off the page does work, as does Dan's suggestion of zeroing out the text in a text element.
Jeff, is there some kind of design reason that I'm missing for why you can't create or delete layout elements directly via arcpy.mapping? This is the exact kind of one-off map composition functionality that makes arcpy.mapping useful, but it's missing. I can't imagine that it would be that difficult to implement (especially deleting), just a few more ArcObjects routines exposed to the Python api...