I am in the exact same s****y situation and I know how much it sucks. I don't know what company you did your private loans with, but mine will do a max 5.5 year education deferment from the day that you took out the loan. So I have decided I have three options:
1) This might be hard, but we might be able to find a company that allows for loan reconsolidation and deferment. Because you are re-doing the loan, there are new terms, and deferment might be a possibility.
2) Ask for the max living expenses during med school. Work real hard to live dirt cheap, and use the money you save to make payments.
3) Calculate the amount minimum payments would be during medschool and save all of this money now, and don't touch it until you pay off those loans. I mean you do have one last summer, so you can work your butt off for three months then to get extra money then too.
I feel your pain, and hopefully we can both make it work. Feel free to PM me, and I will do the same if I find any bank that reconsolidates and defers.
To all you undergrad people out there AVOID PRIVATE LOANS LIKE THE PLAUGE!