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So my batteries put out quite a bit more current than my fixed power supply, which is both a good and bad thing. Good in that the servos perform significantly better when they have enough current, and bad because the PCA9685 roasted with that much current. My home office now smells of magic smoke. Any ideas on how to supply 12 power hungry servos? This was only with the regular MG996R from hobbyking, beefy servos I imagine would take even more power.
Use a LiPo, they are pretty good
Yes, you burnt out the revers voltage protection. You don't really need it if you are careful when connecting your battery. If you want to save the PCB, remove the burnt chip from the PCB (soldering iron), and connect the battery plus with a jumper wire to the plus line of the capacitor. I don't know how thick the PCB traces are, but you may also have to add jumper wires from battery plus and minus to all the servo plugs at the bottom.

Think about it: these servos have a stall current of 2.5 Amps at 6V. If your servo controller happens to position all 12 servos so that they stall, you pull 30 Amps. To withstand 30 Amps (if your batteries can deliver them), you need 6mm^2 cable (or 2.7mm diameter plus insulation).

So if you do this again with the same (repaired)control board, just connect one single servo at firt. Make sure in your software that the servo does not stall, then disconnect, add the next servo, fix the software, repeat until all 12 servos are pulling minimal power.
See my post that covers your question:

https://spotmicroai.org/thread-37-post-185.html#pid185