There are three instances where there’s research to back up a ketogenic diet, including to help control type 2 diabetes, as part of epilepsy treatment, or for weight loss, says Mattinson. “In terms of diabetes, there is some promising research showing that the ketogenic diet may improve glycemic control. It may cause a reduction in A1C — a key test for diabetes that measures a person’s average blood sugar control over two to three months — something that may help you reduce medication use,” she says.
I have patients that have lost tons of weight on keto. They do go off some meds. I also have people who eat a moderate amount of good carbohydrates, and they have lost tons of weight, and been taken off meds, had improved markers, even reversal. I think both approaches work, as I have seen in practice. Many people cannot stay on a keto diet forever. I for one, prefer to have some carbohydrates. I try to pick the right ones. If this works for you, then just be sure to have some medical supervision, which it sounds as though you are doing.
At the end of this 12 week study, scientists observed similar loss in body fat and overall body weight in all three diets. However, they noted that the VLCARB ketogenic diet was “more effective in improving tracylglycerols, HDL cholesterol, fasting and post-meal glucose and insulin concentrations. More specifically, triacylglycerols decreased by 39.9% in VLCARB subjects, 4.0% in VLF subjects, and 9.6% in HUF subjects. 
You'll find lots of free Mediterranean diet resources on the Oldways website, including an easy-to-understand food pyramid; a printable grocery list; gender- and age-specific tips on making the Mediterranean switch; a quick-read "starter" brochure; a recipe newsletter; and even a glossary defining Mediterranean staples, from bruschetta to tapenade.
You say keto is a highly controversial topic. For those of us following a keto diet, there is no controversy whatsoever because the diet proves itself efficacious very quickly. I think the real controversy comes in because the ADA has been recommending dangerous levels of carbs for decades now, and they would lose face if they had to change their recommendation and admit they’ve been wrong for so long. You say there are not many studies on the keto diet, and I disagree with you. You’ll find the evidence if you look for it. Eric Westman, Steve Phinney, Jeff Volek and many other researchers have written volumes about this.
Con: Results can vary depending on how much fluid you drink. By drinking more water, you dilute the concentration of ketones in the urine and thus a lower level of ketones will be detected on the strips. The strips don’t show a precise ketone level. Finally, and most importantly, as you become increasingly keto-adapted and your body reabsorbs ketones from the urine, urine strips may become unreliable, even if you’re in ketosis.