If I understand what you are attempting correctly, you would like the dropshadow to be less distinct, and to appear
as it would if it were falling against the ground as backdrop or object?
I am not certain that Illustrator can provide the 'ground' shadow effect, ie., altering the angle the shadow throws.
You should always be able to control the 'distance' and the 'blur' (fuzziness) of the shadow, as well as it's prevailing coloration. Blur can be further complimented when used in conjunction with the % opacity settings.
The dropshadow options permit you to set the X and Y offsets, and thus control to some degree how the shadow 'lies' beneath the object; blur and opacity, as well as color and darkness refinements, are also accessible at this stage.
There are third-party filters which provide effects such as the 'ground' shadow you have described: I believe Eye Candy's latest has this option. If you have Photoshop,
especially Photoshop 6.0, you will have greater latitude in working with the filters, as well as ease in shifting the angle and direction the shadow falls. Bear in mind that Illustrator is not primarily designed as an 'image manipulation' application, but more so for print design.
It is often easier to perform techniques of this style outside of Illustrator and then import them.
Good luck with your endeavors.