Use the methane hydrates that blocked the flow of oil in the first dome to freeze the BOP preventer and liquid inside the containment dome. Instead of having this be a hinderance for the subsea leak stopping, use it to our advantage.
From Wikipedia on Methane clathrate:
In the less common second type found near the sediment surface some samples have a higher proportion of longer-chain hydrocarbons (<99% methane) contained in a structure II clathrate. Carbon from this type of clathrate is isotopically heavier (δ13C is -29 to -57 ‰) and is thought to have migrated upwards from deep sediments, where methane was formed by thermal decomposition of organic matter. Examples of this type of deposit have been found in the Gulf of Mexico and the Caspian Sea. See this listing in wikipedia for additional information