Yes. Your body is insulin sensitive when running, but once you get above a certain BG, a lot of that goes out the window, as your body responds to the stress of the high BG and you become more insulin resistant.
It is the same reason it is harder to correct a 300 than a 150!
There is never a good reason to purposefully go high or spike before exercising, unless it is an exercise that does not allow you to eat while doing it. Like swimming.
You can try the GU’s like I sent you with your Christmas present. Or try Huma Gels.
The Huma Gels are really really my favorite, of all the running gels I have ever tried.
Get some Huma Gels! Lots of different flavors, and some of them have caffeine!
Good, try the lowering Levemir and see how it works for you. And compensate by not taking as many carbs throughout, but just taking a few as you feel that you might be needing them.
Remember this thought we’ve discussed before - there are two things you need for muscle glycogen replenishment, carbs and insulin. Either one alone does not do it.
I take a lot of insulin after I run because I have had a suspended pump for a while. If you are on Levemir, you don’t need as much insulin, but you will still need some to allow those carbs to be used when you are finished.
Dark side! 
It’s all good. Suffering is an extraordinary teacher.