Honestly, I'd say mounting it to the direct die is a bad choice, because of the fact that it can crack the actual die of the 3770k, and that's another $300 out of your pocket. I don't think there would be much of a difference, at the most probably around 5 degrees.
As for mounting, I dont know if the H220's spacing would even work with out the heat spreader.
As for mounting, I dont know if the H220's spacing would even work with out the heat spreader.