Radius Inside of Stroke

From the way it sounds, I would expand the green stroke into editable paths. Then release the resulting compound path, delete the interior lines I didn't want to keep and apply the blue fill to the objects I did want to keep. It doesn't look necessary to have duplicate interior objects. Just arrange the green objects behind the blue ones in the object stacking order.

For what it's worth, even though the interior lines of the green stroke are sharp in the corners that kind of result is correct for that kind of corner radius. The more curvy blue shapes do not uniformly follow the green stroke because the curve radii in the corners are too large.