Use a higher-dimensional noise (3D or 4D) to directly give you your height samples on the sphere (which can then be reprojected to a flat map using the projection of your choice). This technique also has no seams anywhere.

Another choice for working space is to use a square with the north and south poles at opposite corners. It isn't exactly perfect, but it's much simpler to manage if you're trying to paint onto the height field.

A popular choice is to use a set of height maps rather than a single height map. A basic cube map works well because the 6 sides can be done as individual height maps or they can be done with a single map (that loses a fair amount of space).