Without seeing your house and your stuff, there's not a lot of specific information to give you.

If your office is in the bedroom, maybe you need to find a way not to allow the bills to go into the kitchen?

I agree that the family room should not be the homeschool room, but could your office move in there?

As for the homeschool room, maybe there is space for the books by building shelves that start above the furniture and go up the wall. The less used ones would be out of reach without a step ladder, but still in the room.

We have too many books to have them all in one room (well, we could turn a room into an entire library, and I admire some of those rooms when I see photos, but just havent' been inspired to do that in any one of our current spaces), so I have tried to use bookcases and shelves appropriate to different rooms and have some semblance of a plan for a type of book in different places. Poetry in one place, gardening books another, a lot of fiction alphabetically on a couple of large shelving units, and so on. Books actually add a lot of warmth to rooms, but the trick is to be able to remember what you've got where.

I would think you could add books to your family room easily--with photos and a few special objects--but you would be the one to know WHICH books would go best there.

Also, if you have a good storage unit there, such as for games, movies--you might be able to store certain less often -used items there.

So, one question is, do you absolutely not want to use your family room for any of the storage or activities, or do you lack the right furnishings to help you do things in that room that would be fun and appropriate to do? Lots of times, that's the problem for me. But, for home schooling you may be trying to create and maintain a certain type of separation. I just have experienced with my kids in school out of home, that our family room was the designated area for certain projects and crafts and therefore a few related supplies, and also homework and computer use, though I kept a lot of school and office supplies in another area.

This is not intended to say you shouldn't pursue your one room-itis, but you might be able to think of some things that are a lesser priority for the schoolroom. Then the alternative is, as above, to see if you have yet to make the best use of your schoolroom space with vertical shelving, better storage units, and so forth.