Cat Scratch Connundrum

My cats like to scratch things that aren't for scratching. They know how to use the post (a carpeted cylinder with holes they can physically fit inside) but choose not to use it most of the time. Granted, they do use it when prompted, but only because I basically force them to. It looks sorta like this, but less fancy:

We've tried an emery cat scratcher. All they ever did was sit on it. Now it sits in the basement collecting dust. (Note to self: give it to Value Village the next time I'm by...)

We've also tried a sisal scratcher that hangs from a doorknob. They either don't like sisal or don't like scratching on that part of the door.

Since Paul installed new doors upstairs, Buster has taken to scratching the new frame in one particular spot. I actually found some feline fingernails lodged in the scratch marks. Missy prefers carpet. Since the only "carpet" on the main floor consists of an area rug in my office, she scratches it. The both used to go at the rug in the living room, however I found that Casey was peeing on it when we weren't looking... Both cats have also scratched the arms of our new vinyl sectional sofa in the basement, as well as the backs of our other furniture. So frustrating.

Something that we discovered though is that Buster enjoys scratching at the foam mats that Casey's crate sits on. Luckily for him, I don't actually mind as they are cheap and very replaceable.

So, after I had this epiphany (that I could get him to stop scratching my door frame), I placed one in my office in the same area that Missy scratches the rug. They both went at it within a half hour so I would say it's a success. Much better than all those other places that I hate them messing with!