Wow that's insane. For me, if I sleep too late, regardless of how much I sleep, I still feel tired. But I'm definitely not a morning person because I just hate going to bed early. It might be a work thing too, idk.
You might try intentionally getting excess sleep and going for a reasonably high intensity run as soon as you get up. If you do decide to test that be sure to give it at least a few days to adjust before coming to any conclusions.
Cycling helps reduce my migraines. Starting a ride as they come on is still effective, but ideally I’d go before I feel anything.