My thinking is as follows. The Payne rearrangement you are showing you wish to have occur is simply an equilibrium. It will give the most stable product. If you had a series of alcohols, you could migrate your epoxide from one end to the other. Since you have two alcohols that can react, what factors are present that indicate it will result in the epoxide you have shown? Could it not react with the bottom OH-group? If the Payne must open at a tertiary center, then why couldn't the oxygen also open at the tertiary center of the new formed epoxide?
Thinking further on this, I've never made an epoxide in which the halide as tertiary. Will they form an epoxide or will it simply eliminate to an allylic alcohol?
Ugh, I just realized you wrote your synthesis backwards. Okay, if success of the Payne requires opening the epoxide at a tertiary center. The newly formed epoxide could react with the bottom OH at a secondary center. I will guess the rate of this reaction will be faster then opening of the epoxide at a tertiary center. Won't this equilibrate to the epoxide at the bottom? What about the other two OH groups? Can either of them react?
If this were me, this is what I would do. I know there are a number of compounds with similar functionality. I would review as much of this chemistry as I could. I would take note of which reactions worked the best and which ones merely succeeded. I would try to use what I learned to propose new chemistry. After a talk with my boss, I used to keep the phrase, "Stick to what you know will work" on the glass doors of my hood. I too had a lot of good ideas, but my boss also wanted to see progress.
Okay, I am going to go one step further and ask you to do some library work. I have written a simple model of your reaction. You are proposing the reaction to go to the center. I think it will go to the right. I think the center compound is a known compound or ought to be. It is the epoxide of the bromination of isoprene and then treated with base. Is this a known reaction and if so, what is the product?