The scent thing that eshterchaya mentioned is called Feliway. The aromatherapy device and oil together are quite expensive. I'm out of the oil, but I have one of the devices, if you want to try it. I think the oil costs about $20 - $30 at Pet Supplies Plus in Burlington. With the device it's somewhere between $40 and $60, I think. You can also buy a Feliway spray, but I found the spray really offensive, while the aromatherapy oil was hardly noticable, to me at least. Don't know for sure about the cats.

Since you're confident that it's psychological, have you considered medication, as amberdine suggests? It's not ideal, but if your vet thinks it might help, it could be better than having to change the sheets and mattress protector every day.

And, no kidding, there are animal psychologists. I'd hate to think what a visit to one might cost, but again, there's that, and there's daily sheet-changing.