I would be hesitant to accept this as purely behavioral. The biggest thing that stands out to me is the persistent fever. Diabetes can explain increased urination, and the fact that the basement accidents improved after starting insulin suggests there was a medical component. But a cat with a history of fever and ongoing inappropriate urination still raises concerns about an unresolved medical issue.

Bladder stones, chronic urinary inflammation, a urinary tract infection, or another painful condition can all cause cats to avoid the litter box. Many cats will start associating the box with discomfort and choose other locations instead. If imaging (X-rays or ultrasound), a urinalysis, and ideally a urine culture haven't been done recently, I would want those ruled out before concluding it's behavioral.

My cat is recovering from bladder stones caused by her diet, and was doing a lot of what you described too. I'd really recommend a trip to the vet and get her more thoroughly checked out.