Your shading effect looks pretty good.
If you want more steps without adding shapes, you can use shadows. Each circle appears to be about 102% larger than the one above, so, if you add a shadow to each circle, with zero offset, and 101% larger, you'll get 2X as many steps.
To the top circle (smallest) add the shadow, size =101% & no offset, select the darkest gray you want, and make the shadow 50% transparent. This will help blend it with the cirlce below. For the next shape down, select the fill to be one step lighter than the previous shadow above it, and set it's shadow to be one step lighter, again, 50% transparent. Work your way down, progressively going lighter and lighter. For the bottom (largest shape) you will want the shadow to either be only 20% or 0% transparent. The 20% will allow a small amount of background to show thru. May not be desireable.
This provides a linear gradient. To improve the rounding effect, you could vary the circle and shadow sizes such that the upper circles have greater extension than the lower circles. Hope this makes sense. (Uh, for example, the 2nd circle might be 108% larger than the top circle, the 3rd circle 104% larger than the 2nd, circle, and 4th circle 102% larger than the 3rd, etc.) Likewise, you could change the amount the shading changes, such that the upper circles have less change than the lower circles.
HTH
Wapperdude