Thanks for the disassemble instructions! 🙏It's so nice to see what is inside before talking it apart.
I just soldered in two off-the-shelf 900mAh NiMH batteries into mine. I added some wires to the battery terminals instead of trying to work in that tiny space under those restrictions. There's plenty of room for those wires under the water resistant hood.
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The trick to solder on the batteries (or wherever) is to add flux. It makes it super easy (not pretty, but easy).