Of course, the objective is to get to a whole-earth scheme. I'm going with a projected cube approach, where the basic seamless algorithm is run on the six sides of the cube. I like the Quadrilateralized Spherical Cube which was developed for processing the data from the NASA Cobe satellite. A nice property of the projection is that is equal-area, so that a recursive devision in the cube face space should result in 4 equal-area spherical quads on the earth. It looks pretty:
Here's hoping that the calculation of the projection doesn't become a big bottleneck. Incidently, it was very hard to find the equations describing the projection: I eventually found a nice formulation here. But beware: there's a typo in Equation 3-38. "cos(theta)" should be "cos(phi)."