I hate this also. That's about 8 thousandths, if you have some old automotive feeler guages laying around you can cut one (prefer brass) to use as a gap filler. If you use a .003" or .004" cut just the width of the nut, and wrap it round both flats to protect the finish. What ever size works, really.

Also, I feel headsets are often overtightened, and sometimes just an extra tweek past snug is plenty if everything is clean and serviceable. Then, just re-check after one or two rides.