Didn't see a mention of Unitek. It is (or was) a company that made precision capacitor discharge welders for smallish work. They used to be common tools in physics labs for welding wires and foils made of refractory metals. I think they were probably developed to assemble vacuum tube internals.
Don't know if you could still find one, but it seems to me it'd be close to ideal for welding directly to battery cells.
HTH,
bob prohaska