There is DP and also feet on the floor, which means it rises after you get up. Because of the hormones that cause this, they also cause insulin resistance for a few hours after. It can make it very stubborn to go back down.
I am a type 1 LADA, I do not low carb. I just usually don't eat in the am as it's just too hard to control blood sugars until about 11 am for me. But if I eat anything, even low carb I will spike up and need much more insulin to get it to come down.
I am not familiar with your type of diabetes. But I believe it is a deterioration of the cells that make insulin? So does it stabilize or will you lose all insulin making function? If you stabilize you might be able to skip adding more insulin but if your ability slowly keeps getting worse you will need to add fast acting somewhere along the way and carb count.