I would suggest that primaries should not use state or federal resources at all in primary elections since this is merely the party members chosing who will represent them in the general election. Thus the parties whould be responsible for gathering the votes and should not use taxpayer funds in order to do this. It actually presents a conflict of interest between the government and the parties. In my view there is quite a good argument that the entire practice of handling primary elections in any official capacity is completely unconstitutional.
Only the general election should be handled by the State.