I kind of know what your going through. My head shape is kind of odd too. It isn't noticeable when I wear a hair system or a hat, but bald you can really see it. My head is kind of elongated up top. And I always had a high forehead to deal with.

Perhaps you can use a different hair style to transition. For example maybe wearing your hair down in bangs for awhile. The jogging is a good idea too. u can wet your hair and have it down and i don't think anyone will notice.. than make your transition slowly. I always wore a hat.. hell people used to always bust my balls about wearing hats so much. But that is MUCH better than them seeing you completely bald one day and the next you have a full head of hair. I am happy I wore a hat a lot and concealers etc.. It helped me with my transition. If people ask why i always wore a hat or why my hair was funky.. I just say when I was younger.. which is the truth i had really crappy hair.. but as i got older it started getting straighter and better.