Andy, those "big honkin' 6v lantern batteries" in the carbon-zinc days contained four "F" cells. "F" cells are about "D" cell diameter and twice the length for a proportional increase in current/power. I've a feeling that you opened up a substandard lantern battery. The expensive alkaline lantern batteries feel heavy enough to contain "F" cells.
This brings to mind the cheating that goes on in the rechargeable industry when you compare NiCd batteries. If the "D" version has the same current output as the "C" version, you have a problem, for they have a "C" cell in a "D" case and trick you into thinking that you're going to get "D" performance.
Dean