This is what I would try. Never actually done this, so no promises. The only problem I see is the formation of the alkene... If the methyl protons (not part of the t-bu part) are acidic enough due to the Br, a strong non-nucleophilic base should cause elimination to form the alkene. I like NaH because the deprotonation is irreversible and would go to completion. For deprotonation of the methylthiol, a non-nucleophilic base protects from unwanted addition to the chlorinated carbon. Its possible that there is a much better way to do this, but it might be worth a try! Hope it helps!