I think you're proving my point about getting caught up in "open primaries" or "closed primaries"...
Shouldn't a party be able to determine it's own means for selection of it's candidate? If they allow open elections, the the public gets to choose their candidate (however the party has been known to take an elected nominee out as the repubs did that in 2004 in IL which allowed Obama to become elected to the Senate and eventually the presidency). Crossovers become a problem when one party has a strong candidate and can afford for some of its members to vote in another party's election. I'm not sure how to fix this system. However, some states ( I believe ME and NB) do a proportional allotment of electoral votes.
My point is that if you have no party registration, then the party itself has a lot more control over how they elect their candidates. Here in VA, the District decides whether they do a primary or a caucus or as many as three other options. So I agree that a party should have some sort of say so on who they have represent them. The question is always: how much does the party leadership have say so vs. the "rank and file." I'm not comfortable making that uniform in all 50 States and all Districts.
This is why I'm NOT a supporter of Proportional Representation. We have PR here in the U.S. at the Town Level, even in VA, which does not follow the New England "township" model, but doing that at the U.S. Congressional level indeed DOES have Constitutional implications, and it would likely force all 50 States to have COMPLETELY identical election setups (just like Term Limits). It is also a MONSTROUS SEA CHANGE for how Congress is elected, regardless of Constitutionality.
I think the three I laid out does provide some flexibility, but they're already being done in some states in different combinations, so it can be done in more States. This will not solve all problems, but I do not think that they contradict each other in any way. Number 3 is made a little more complicated with no party registration (number 1), but there are a variety of ways to handle that, and if it means an extra election or two, I'm all for it.
Good things...