Some clarifications:
I used loose bearing balls, 5/32 in size.
Fort the parts that are essentially attached to the bike meaning the races and cups, I just cleaned them of old grease and did not remove them or do anything else.
The headset seems to be turning normally.
I have not checked that the locknut is going as far as it can, I will try check that tonight.

I think I'll take the whole thing apart, tap down the cup, and reassemble it tomorrow. If there is still a space, I'll head over to the lbs for spacers and hope that fixes things up.

Thanks for all the feedback and ideas. Although, it does seem like most of the potential problems should cause there to be less space not more.