From inspection, the two terminals in the centre just connect together, so a circuit is made between the 4 AAs. So if you were to find some suitable material and glue it to the base of the middle two battery slots in the tray, completing the circuit that should work. Either two separate pieces connected with solder and wire, or just one strip between the two. Have a look inside some old knackered torches that are most likely lying around the house for suitable bits, or failing that, thin tin or copper sheeting.
I would think that will work.