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Okay, so we're coming from a different curriculum where we could just choose one read aloud set and use it as a family read aloud for everybody.

Is that true with Heart of Dakota too? Or do you make a point to read each child's assigned read-aloud from the Storytime box everyday? I'm specifically looking at Little Hearts or Beyond and Bigger.

Hod is not set up that way, but depending on the guide, it is easy to combine.
In LHFHG, storytime is mostly Burgess books. These have very short chapters, which are great for getting kids used to listening to books without pictures each day.
In Beyond and Bigger, you use nine books to cover the nine genres of literature. There are the book packs for each guide to pick from as well as additional suggestions in the appendix. And you can pick your own books as well. The Beyond suggestions are shorter than the Bigger suggestions in general, as they should be able to sit for longer readings as they get older.
In Preparing, storytime is tied to the history. So you are reading about roughly the same time period in a fiction book as you are in the factual history books.
CtC offers a history set similar to Preparing and then a boy and girl option similar to Beyond and Bigger.
They RtR through MtMM have history storytime only, similar to Preparing.
The high school guides have a living library, which can be used as storytime (adult reading) or independent reading (student read).