How to create a cube map of a circular arena

I’ve created an arena and applied textures to it using Cycles. Now what I’m after is to create an interactive model that you can rotate. The idea being that you can drop 3D models into it and rotate the arena to give a better look at the arena.

I’ve tried to create a cube map multiple times, but due to the circular shape of the arena and the camera distortion, the end result doesn’t work. I need enough of the ground and the area of the sky visible in each part.

Worth mentioning that I’ve also tried exporting as a .glb / .gltf file but the file size is too large for use.

Can anyone help me figure out a way to make sure the entire arena can be combined into a cube map without the end result being distorted?

Here is a way to do so: Rendering a cubemap/skybox

But why dont use just the model of the arena, it will give a better result?