Sorry, it took so long for me to get some time to look at this. I've been busy doing a laundry room remodel.
The first thing I did was to click on the outer most polygon and the ambiguity popup showed three polygons, two were white filled and the third was blue filled. My response to this was to delete all the polygons and restart with just the basic geometry. The best approach to this is to start with the inside small objects and work your way out. I began by filling all the circles, then the slots. Next, I filled the etchings, found numerous geometry errors as I moved through them. I'm posting some example screenshots. I then filled the polygon for the space between the etchings and then the board.
When the geometry won't fill do a right click on one of the lines and in the popup menu click on "Select Chain" and see if it will go all the way around, if not zoom in and check the points where it stopped. Another tool is "Repair Curves", and again do a right click on one of the lines and click on "Select Chain" and look for errors. The select chain thing also works with the "Fill" tool, select the "Fill" tool then right click on one of the curves and select chain. If that doesn't get it then select the "Fill" tool and shift click each curve. Filling the "donuts" around holes required holding the shift key and clicking just inside of the outer circle then release the shift key to fill.