maybe you could pipe air in from the sides, through the frame?
I just searched and it looks like no one's tried that. or at least they haven't posted about it if they did. To be really worthwhile, the bike would have to be dyno'd with and without the tank lift, and then with and without the airbox mod, to answer all of the questions floating around here. And then again maybe with and without the alien invasion prevention mod? :BLAA: In any case, we'd need a forum member who knows a friendly dyno shop. If 25 ppl contributed $25 to the cause, that might get to the neighborhood of the cause. But I'm not sure that you're allowed to share maps. And the non-dyno'd participants would all likely be slightly off, just 'cause every bike's a little different.
Wasn't there a guy on the Ninja forum who did that? I seem to recall a much ridiculed Ninja owner who cut his frame in the pursuit of improved airflow. It'd be worth finding out if he's still shiny side up and on the same bike.
As for keeping the engine heat away from the box to begin with, how many of you have had that rubber flap thing off the engine top? Applying a layer of insulation there would likely be a good starting point! Keep the HEAT OUT!