There is no such thing as a 2-tier casket.
Go to google or bing and do an image search for casket. My goodness! - there are hundreds of photos of caskets and every single one, without exception, has a flat top for the base, with a flat corresponding bottom for the lid. Every. Single. One.
There is a slightly sharper version of the church photo. Download http://www.hawaiicatholicherald.com/wp-content/uploads/2013/12/1lorettafuddyfuneral.jpg. It may be more obvious there. On the back left of the casket is a hinge. It’s obvious that they have aesthetically draped the casket lining over the hinge to hide it from the mourners. You can see that the casket lid has a large puffy-liner around its inner edge. Look at the puffy-liner on the lid where it connects to the base of the casket. The puffy-liner stops at the base which appears to be just below Fuddy’s folded arms. That’s where the lid connects to the base.
There is only one casket and the church’s photo shows the same casket as the videos.
By the way, there is a bit of brown near that rear hinge. That is clearly the candle stand behind the casket.
That image has clear angles on it just like the image I linked to from here. I drew a red line parallel to the actual lines that we see. There are clear angles, which I pointed out clearly. You can’t just wish those away.
It may be a piece of cloth of some kind to hide a hinge; I don’t know. It sticks up straight, stiff, and square when the lid of the casket is open, so it doesn’t seem like a drape. In any event, it should be there in all the views where the casket is open.