You might find this fun. There this sonic the hedgehog special stage from sonic three that takes place on a sphere. Recently I made a remake of it and they project a 2d grid onto a sphere, but the projection adjusts as you move, so no matter where you go, you never end up at a pole. The poles always stay on your sides.

The other interesting bit is that you can have an arbitrary map size and just repeat it. The game is 32x32 but it could be whatever.

https://blue-sphere.fly.dev/play?map=s3-01

Anyway, great stuff you have here!