Howzabout limiting participation to real New Hampshire citizens? Let's not allow busloads of out of staters showing up on election day to vote. Out of state college students should not get to vote in New Hampshire, they can jolly well vote by absentee ballot in their home states.
And for that matter, the primary is how the parties choose who the party will support with money, publicity, and workers. Primary voters should be party members. If a voter cannot bring him/her self to simply declare their party affiliation when they register to vote, then they should not get to vote in party primaries. It's not like the parties ask members to do anything, like contribute money, attend party meetings, post yard signs. They just ask the voter to express an interest in the party, verbally. I'm thinking that voters who cannot say "I am a Republican" or " I am a Democrat" are so turned off by American party politics that they should mot be allowed to mess up candidate selection by voting in the primary.
Speaking of which, NH voters should be required to register, in person, at town hall BEFORE election day. Voters so unmotivated as to not get down to town hall and register at least a week before election day, are too lackadaisical to cast intelligent votes. And requiring registration in advance will make it harder for out of state shills to vote, they will have to come up twice, once to register and once to vote. To register the voter needs to show a NH driver's license, out of state licenses make him an out of stater. And they need to show a real NH address, an apartment or a house, college dorms are temporary and don't count.