A few more things to try. First, I don't mind the little gaps between the infill directions.
If you want the infill to be stronger print several layers in the same direction. Put 2 or 3 lines at 0 degrees in the infill window followed by 2 or 3 lines at 90 degrees. This will add strength without the odd things that happen with high extrusion width.
I print infill every 30 degrees. This acts more like a hex/honeycomb infill and still prints fairly fast. Two layers each at 0,30,60,90,120,150 and it's fairly strong.