Please define 'organic'... Are you talking about cells in a non-rigid container? In that case, those are suspectible to swelling, and in doing so; loosing capacity. Also, these cells are often charged really fast ( >2C-30C), which reduce life considerably.
You'd be better of replacing them with some 'laptop' cells (18650 cells - 18mm diameter, 65mm length), if you can make them fit. Those are more durable, and comes in up to 3Ah (maybe 4Ah nowadays...)
The cells used in my e-cigarettes are 'soft' lithium cells, rolled into a cylinder. These last only 3-6 months... I've swapped those cells with some used laptop cells, and they last several days between charge, and doesn't loose capacity... (so far...
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And charging;
As soon as you connect rechargeable Lithium cells in series, one really should make sure there are a BMS connected (a Battery Management System); one can get a simple BMS for 2 cells for a few $'s... (check the RC market...)
Edit;
2x 3.7V in series would be 7.4V... = 6 AA NiMh cells...
Could you fit that?
I would check the circuit board where the led's are; there's probably a small current regulator there. find the number, and check on the internet what voltages that regulator can handle. Maybe you can run it directly from a 12V battery...