I'm trying to create a simple animation of a Lego plane flying, with a backdrop of clouds scrolling past the camera. What's the best/most correct way of doing this?

I thought about a few possible ways. I tried using the world environment by applying the standard HDRI background and using the Light Ray node option "is Camera Ray" to mix in a cloud texture. However, I can't find a way to disentangle the two textures so that I can render the backdrop, render and denoise the image of the Lego model, then composite them back together (I don't want to denoise the "is camera ray" backdrop because it's procedurally generated and works fine as is).

I tried using a textured plane located behind the model, but I have trouble getting the cloud texture UV coordinates to scroll properly, and it also forces the camera to be locked in place, as if I move it then the edge of the plane comes into screen. I also tried just using a giant textured plane that is animated to move past the static camera, it sidestepped the UV issue but is really awkward to set up and use.

I'm aware that video games tend to use skyboxes or sky spheres, but I can't figure out how to set one up in blender, and I worry that a physical sphere will block the HDRI map light rays.

I feel like I'm missing something really obvious here. Any suggestions?