I saw your post earlier and tried finding the crib vibrator I used years ago online. I don't remember the brand name and it was 13 years ago but it worked great. It was battery operated. Took four D sized batteries and attached to the side of the crib. Just a simple green and white plastic device. It didn't make sounds, only vibrated. My DD loved it and it was the only way my ex-DH could get DD to go to sleep.
I searched for it online and I didn't find one exactly like it. I'll take another look. We paid like $90.00 for it back in the day which I thought was expensive at the time but it was totally worth it.
Now if only I could recommend a current model. If you can find any one with a good review it will probably be just fine. Cotton Puff sounds a lot like my DD so I think it would really help her.