Use lines instead of fill by creating several concentric circles in the area you want to fill.
Start by making the outer circle. Then using the offset tool, create an interior offset at a very small distance. Then you can use Ctrl+offset to replicate that over and over again until you have made the number of interior concentric circles to create the boarder you are after.
Another technique is to use Z offset in combination with the above and unfocus you’re laser out to effectively create wider lines to speed that process up even further.