Where to get solid aluminum "battery" replacement cylinders?
Why are you making them out of metal???   Make them out of wood.  Much easier to find a wood lathe than a metal lathe.  

Just cut it about 2mm short on the active ends, predrill a small hole, sink 2 washers and a wood screw, and attach the wire between the washers. With screw, washers and wire, it's the same height as an AA.  

Beware drywall and deck screws with insulating coatings.  Brass screws are a good choice.