Just to clarify.
I did not draw that image, it's just an example I posted because I noticed the heavy banding.
And yeah, I think gradients can look cheap if they're too extreme. I like the softness they add if they're subtle.
Your edit is great, but I've realized that I really do need the flat style I'm using at the moment.
Cell shaded would be the best way to describe the style. I think if I started with gradients I'd run the risk of things looking too real.
Here's some stuff I'm working on at the moment.
I've noticed the more I think about how the shading looks the more it confuses me.
I thought the tire looked hella weird, looking at it now I think it's acceptable.
These textures will probably be seen at half size too.

Biggest problem for me atm is just keeping this style consistent, as you can see on these images.
Feels like the only thing making them fit together is the outline and lack of color.