I agree. Earlier is definitely better. You can check with the school to see if earlier dates open up (but don't be annoying). Slots don't open up too often early in the process, but it's quite common after the first round of acceptances on DEC1.
Some schools will tell you if you are interviewing for a slot in the class or an alternate slot, and some don't.
For example, I was invited for an interview by a school in OCT, but when I called to schedule, the first available date was in March, how frustrating. But they also told me on that call that it was for a seat in the class, essentially meaning it was mine to lose at the interview. So even though I would have interviewed late in the process it was still for a seat in the class. So a late interview is not neccessarily bad.
Shortly after 1DEC I called them back and was able to get an early JAN interview, and was accepted by Mid-Jan. So it all worked out just fine.
Good luck!