Change your mindset and enjoy the feeling of space. I am from New Orleans and the old mansions are not loaded with furniture. Get a few pieces of large scale furniture that takes advantage of the height.

You can also add large crown molding at the ceiling. Try molding that is deep, like 8 to 10 inches.......Maybe even 12"....(bring samples home and try them out)

At the floor you can add tall baseboards, also 8 to 10 inches. The molding should be painted a glossy or semi glossy white.

Paint the walls a rich color in taupes or sages or warm buttery tones, or even red.
(the ceiling should be a creamy color)

Also add large area rugs that define the rooms by being almost as large as the room.

Using big, bold pieces of furniture is also a great idea that saratogaswitzzlestick recommended above.........

Forgot to mention how lucky you are to have 12 foot ceilings.......

Grand furniture can take up some of the space. Dropped light fixtures such as chandlers can also create an illusion of a lower ceiling and not feel so empty.
Do you have any photos of the rooms? Could recommend furniture designs and/or lighting styles that could help.