Here's an update to my post.
The status on my iPad finally changed to "Shipped" this morning, and I received a shipment notification email from Apple. So here's the period I waited under each "status".
March 15, 2012: Order placed.
March 15, 2012 - March 27, 2012: Status "Processing"
March 27, 2012 - March 30, 2012: Status "Preparing for Shipment"
March 30, 2012: Status "Shipped"
However, there is a problem. As I mentioned in my previous post, I had changed shipping method to Overnight Shipping. This means next business day delivery. I also had Overnight Shipping on my iPad accessories (cover and camera cable, which I indeed received the day after they were mailed). Since the iPad was shipped today, Overnight Shipping means I should receive it April 2, which is the next business day (since March 31 and April 1 are Saturday and Sunday).
However, the shipment notice says it will be delivered by April 4, two days later than it should arrive. So the total shipping time is March 30 - April 4, which is 5 days instead of the Overnight Shipping I was promised.
I noticed that when I received the iPad accessories (which actually shipped Overnight), the shipment tracking page said:
Service Type: Standard Overnight - Indirect
However, for the iPad itself, the shipment tracking page says:
Service Type: IP Direct Distribution - Indirect
I don't know what this Service Type means. It's obviously not Overnight, and that's why it's taking 5 days to arrive. I have no idea why Apple changed this, since I was promised Overnight delivery.