It's been many years since I got my passport, but your description of the steps so far seems about right. Yes, it's a bit ridiculous.

What's more ridiculous is that lead-time. You'd think that the people who organized the prize giveaway would have taken passports into consideration. It usually takes longer than that to get a passport. I think you can pay extra for a rush job, at least that's what I recall from when I got mine.