Generally speaking, a banding issue is the result of too much space between too small of a difference. The addressability of the image setter doesn't have enough points (data) to smooth it out.
Within InDesign, see how much more shading you can introduce and maintain the look and feel. So if the darkest is, say 80% and the lightest is 70% and the size of the circle is about 2", then try going from %83 to 67%.
What I always did when I had any banding was create the gradation in Photoshop then add 1/2 pixels of random noise via the Add Noise filter and that always solved it.
With only 256 shades of gray in Postscript, trying to stretch a gradation of only 12% or less difference in shade over a large area, you're going to get those hard edges because there just isn't enough room for the gradation. The noise provides 'relief' of sorts to maintain a gradation rather than a hard line.