I'm sorry about the mystery ailment. My vets here have always said that you feel like there's something off with your kitty, there's something off, because you know your kitty better than anyone. Unfortunately, with cats, the same symptoms can be indicative of so many different issues, and it seems like quite often, vets can't make a definitive diagnosis, despite testing. One of my kitties passed away a couple of years ago just 10 days after a vet visit where we had all sorts of tests done that came back normal. I knew something was wrong - we just didn't know what, and we still don't know the cause of death.
I don't mean to scare you, just saying that it's entirely possible that something is not right, despite all evidence to the contrary.
The purring and lethargy could be related to grieving for the loss of her kitty companion. My kitty grieved for over a year. Lots of extra time and cuddles might help. But the staring off and seeming confused, and just sitting in her litterbox, don't seem like they could be related to grieving. Did you mention these to the vet? Could they be mini-seizures? I believe that seeming confused, even without other physical symptoms, can be a symptom of a seizures in a cat.
What kind of additional testing did the vet think might help? Just the things that you mentioned weren't already done, or more on top of those? In addition to what doodlebug's already recommended about doing all additional testing and consulting a veterinary school, I'd ask the vet about a couple of things. I might be going overboard, because my current kitty has kidney disease, but I believe that regular bloodwork won't necessarily reveal very early kidney disease. If the SDMA test was not done as part of the bloodwork, I'd ask for one. If it shows anything, then a urinalysis has to be done as well, in order to try to accurately determine the stage of the kidney diseasea. In that case, a blood pressure check (which not all vets are necessarily equipped to do) is also important, since kidney function and hypertension are related, and one common treatment for cats with kidney disease is blood pressure medication. I'd also ask whether a dental xray might be useful since the vet couldn't get a good lookat kitty's teeth. There may be an abscessed tooth in the back that's causing some discomfort.
I hope that additional testing and consulting a veterinary school will help to get at a diagnosis.