The costs of open primaries can be kept down by limiting the amount of money that each candidate has by the way of campaign finance reform. Also a good way to cut the costs of open primaries could be to reduce the amount of available spend per candidate in any district based on the per capita income if the constituency.
Anything the government so much as breaths on, most of all federal, can be reduced 70-99.9% without much thought at all to the subject matter. The amount of money dumped on this garbage is truly breath taking to behold. Primary cost probably wouldn't even make the top 1000 and even that is completely ridiculous.