Nonsense!
Most period 1" headsets use 5/32", or in some cases, 3/16" balls. The trick is to fill each race up, then remove 1 or 2. Typically you'll be left with 24 to 26 balls in each race.
Also, getting a top nut shouldn't be a problem, as you know the thread you need. The only thing you need to watch for is the nut bottoming out on the top of the fork steerer before it hits the spacers (or other locknut in some cases).