Its important to consider amperage discharge too. Can the two 18660s put out the same current as the big rectangle one?

Replacing the old halogen with led would be a big difference. Ot would need basically no amperage. At that point you can attach usb male to alligator clips, clip the ends of the lanterns battery pack connectors to supply 5v 2.4a of power directly with a power bank.

I use a 5 volt led bulb that plugs into regular usba slot. It works with small power banks and ast forever on larger 20ah batteries.