Is a mini LP really 7 inches across? I know that it is a Hybrid SACD so it must fit into a standard CD player. Just curious.

Afaik these are shm (super hard material) cd's or sacd's in a booklet.
I own a few shm sacd and cd from cd Japan
The discs are 5", the cd's playable in any cd player, the sacd's ONLY in sacd compatible players as they are purposedly single layer as pure as possible hard material and thus either sacd only or cd only. They even have a green lacquer to reflect the (infra)red laser as good as possible according to them.

Personally i find the styrofoam inlay of the booklet pretty unhandy and have taken out the sacd's and cd's and put them in jewel cases i bought seperately.