We've had success with the new end table containing the litter box. The entry is large enough for even the pudgy cat to fit inside. The high sides of the litter box inside keeps our Sadie from peeing over the side of the box, in fact, so successful that I've replaced two of our extra large boxes with two of the high sided boxes. We've left the door of the end table half open so they would get used to going inside and now we only close it when we have company which was actually the reason I purchased it in the first place, to hide the litter box from company. And it certainly looks good, so good a guest recently expressed interest in buying one for herself.
I have also reduced the number of litter boxes in the living room from three to two. I sprinkled lavender essential oil where the removed box used to be. I've had good luck keeping them from using the carpet or the mat with the lavender oil. The only place I won't use it is on the mat or carpet leading to the box (that would kind of defeat the purpose). So far, so good. And, last of all, I purchased two new mats (http://www.wayfair.com/Imperial-Cat-Heavy-Duty-Litter-Mat-00104-IPC1046.html) and oriented them long ways so the litter box is at the end of the long side and they have to walk the length of the mat which removes most of the litter from their paws. Our original mats (http://www.wayfair.com/PetFusion-SmartGrip-Cat-Litter-Mat-PETF1001.html) actually hold odor and need to be cleaned often. So, we'll keep them as emergency mats after we've cleaned them thoroughly.
We have also been giving Sadie laxative a couple of times a week because she's depositing little marbles in one box and an hour later in another box. The laxative seems to help her eliminate all at one time. And she loves it. An update with Sadie, for the last three or four days she's been pretty much with me, either in the craft room or following me around. She let me pick her up yesterday for about five minutes, always a welcome surprise. Yesterday she was eating in the dining room and actually brushing Sassy with her tail.