Robert, I think you're making it too difficult. I'm going to add a few assumptions, such as no air, pefectly round igloo, and I am assuming the point you're seeking is referenced to the igloo-earth contact point in line with the direction in which he started.
So... it gets easier if you change your frame of reference. The first step is to calculate how long it takes him to reach the ground moving in a single plane; that's the hard part (but computationally easier than figuring the 3-D trajectory). But once you have that, all you need to do is to figure out how far the Earth has rotated in that time, and that's your contact point.