Looks like your cat prefers horizontal surfaces, but maybe cardboard is not her material of choice. I have one of those cardboard posts at home and my cats totally ignore it
On second thought, could it be that she likes cardboard as the material but would prefer an upright cardboard post?
Another thing may be the size of the posts. Cats need to stretch out as they scratch. You mentioned that the rope covered vertical post was two feet high. Assuming the cat can use all two feet for scratching, it sounds good. But if she prefers the horizontal cardboard ones, they may be too short. They need to be at lease 30 inches long to allow the cat a full stretch.
You'll need to experiment with other posts - how about a sisal rug? Most cats love to scratch rope and it would be a different type of material. Debbie suggests wood - it's definitely a possibility. Eventually you will find a post that would be your cat's favorite. When you introduce the new posts to the cat, never hold her paw and try to make her scratch it. Chances are the cat will be interested in this new addition to your living room and will try it out on her own. If she doesn't just play with the cat around the post and try to lure her with toys to make her swat at the post and discover its texture. Rub some catnip on the post occasionally to make it more attractive.
Your posts' location sounds good to me, as you say she scratches only in that room.
While getting a post that your kitty will like, you should also make her dislike the carpet and your furniture. From what I've heard, the best thing would be to cover the areas where she scratches with double-faced masking tape. Cats hate the sticky feeling under their paws and they avoid these areas. There's a product designed specifically for this called Sticky Paws. It's supposed not to leave a residue behind, as masking tape might.
You'll need some patience, but eventually you CAN train your cat to use only the scratching post.
Keep us posted (pun intended