I always wondered if HTM spheres are a worthwhile solution for lower sized textures. You start with 8 equilateral triangles that make up the sphere and subdivide as needed. You could possibly use a square texture made of 8 right triangles that each need minimal distortion (as opposed to an equirectangular texture).
There are also other interesting spherical tessellations that could be used - one is implemented in Google's S2 geometry library, the other, HEALPix, is used for astronomical datasets:
https://arxiv.org/ftp/cs/papers/0701/0701164.pdf