I'm not entirely sure what this means, but at least with regard to Congressional elections in New Jersey, there was no role for the state judiciary to play with regard to ballot vacations.
2. Does the Constitution speak to the election itself, or also to the means by which candidates will be selected? 3. What effect did the 17th Amendment have on this passage? Did it modify it in any way?
"The times, places and manner of holding elections...." (Article I, section 4) would suggest that the means is also left to the states' legislatures, subject to Congressional changes and the US Constitution. Speaking specifically about the 17th Amendment, that changed the group doing the election from the state legislature (Article I, Section 3) to the people of the state that meet the qualifications of the electors of that states' most-numerous branch of the legislature.
As a side note, the similar section of the Constitution with regard to the Electoral College appointment (not necessarily an election, see Article II, Section 1) was cited in the concurring opinion joined by Justices Rehnquist, Scalia and Thomas.
Sorry, I'll try to rephrase and be more clear...
IMHO, the SCOTUS had to weigh two issues: to what extent the NJSC's ruling had infringed upon the Constitution versus the states' rights issue.
Is it possible that SCOTUS decided the voters of New Jersey will still have a chance to vote for a candidate, and so a bad NJSC ruling did not do such damage as to warrant federal intervention?
As for the rest of your post, I'll check it out soon as I can. May not be today though, things are a bit hectic.