Chiming in March 2025 to say that this is still a good fix. There was an Amazon link for "EBL 3.7V Replacement Sp 803048 Battery for DXR-8 Video Baby Monitors" mentioned above; it's no longer available on Amazon, but EBL's official store does still sell them (with free shipping to the states!). [link|https://www.eblofficial.com/products/battery-for-dxr8-video-baby-monitors?variant=40799757598802|Here's the link]
I got one and the repair seems to have gone well. Charged up and used them for 2 hours, it's going great! Huge relief to be able to use these headphones wirelessly.