Tesla uses li-ion, but for this application you want something like LiFePo4. Expensive, certainly - but also similar enough to conventional li-ion that the existing Tesla production lines should be able to churn them out without too much alteration.
Or you could do it old-school. After all, weight and size are no object - what's to stop you from just using a heap of lead-acids? Really cheap, very long life, and when they do wear out they are highly recyclable.