I figured out a bit of a workaround for this problem which is suitable for my purposes, but may not be for others... If you set the whole background to white and then the axis background to gray and set the gcf "InvertHardCopy" to 'off', then the figure comes out looking more or less right for any situation that requires/allows a white background. This would be:
set(gcf,'Color',[1 1 1]); set(gca,'Color',[.8 .8 .8]); set(gcf,'InvertHardCopy','off');
Attached plot shows this (with some other corrections to the data that are unrelated).
I guess I answered my question well enough for this time, but I'd still like to know whether this can be done in a way that preserves the background as the original "clear" in case I'm interested in pasting my pdf file into non-white-backgrounded documents in the future.