Do not install a spacer. The early bikes had them, the later ones did not.
3/16" is not excessive.
The bearings are providing the support needed, the gap is irrelevant.
Your primary concern is that the drive shaft is not rubbing on the inside of the swingarm.
Secondary concern is that the swingarm is centered in the frame.
To do that, just make the gap equal on both sides. Do not be concerned about the size of the gap, unless your frame has suffered MAJOR trauma.