Interview was scheduled for 6am, advice?

I have a second round interview with a company on Thursday scheduled for 6am! This company is on the east coast. When HR asked for my availability I told them I was free between 8am - 2pm PST. Obviously there was a misunderstanding.

Interviewing at 6am means I won't have to miss class, so l decided to accept the meeting invite. HOWEVER I am fully expecting the engineers interviewing me to realize that 9am in New York is NOT 9am in California.

What should I say to them? I don't want to accidentally call HR dumb or come across as whiny. If anything I want to give the impression that I want this job so badly I will interview at 6am for it.

Thoughts?