I wanted to post my experience in case anyone else is looking for a good replacement battery for the Corsair Void. There are baby monitors made by Infant Optics that use a similar battery with higher capacity (1500mAh vs 1000mAh), same voltage, and same connector. It also fits inside the plastic casing inside the headset even though the battery is a bit thicker.
Here's a picture of the installation. The install was straightforward and I'm so happy that I can keep using the same headset.