Since diagnosis, the ability to run for fitness has alluded me, because of weight problems, and age, I have since losing the weight and more importantly my health, I still can only run a few hundred yards, and I prefer to walk. Maybe because I have always walked, in my younger days, work and for recreational activities.
In fact, I don't need to run because I walk. This way I know I'm not going to get a liver dump. Our bodies are designed to walk, and maybe run, but you can't run all day. Walking helps with digestion and control of your BS levels. At my age, walking is enough exercise for me.
When sports people exercise, they carb up because they are not in Keto, and you will use your energy quicker, because you need energy, but because of whatever is happening with your hormonal response, your body can't cope, so you fast before exercise, but that ain't working, if you carb up, that doesn't work. You are running to be as fit as possible. You don't need to lose weight, but you will, that is natural if eat less than you use.
Because of adapting to low carb, the body takes time to start producing ketones for energy. But from everything I have read, is that you are persevering with having a few carbs, when if you cannot tolerate carbs, like me and quite a few T2s can't, those few carbs are for want of not swearing, is messing you up. I also reckon that the glic has a half life that is also having an effect.
Your next move is to adapt properly to ketosis, and dump the carbs and glic. And test and record all your meals, and see if you feel better not doing the strenuous exercise, because you never know it could be the hormones that you need when you exercise.
Keep safe