I dont see how a higher output capable brick or USB source could possibly burn out the charger.
The amps are what the charger brick/source is capable of outputting, not what its pushing into the device that is connected.
That is not how electronics work...
If the brick is rated to 2.4A, but your device only uses 500mA, then it will only draw 500mA.
If your brick is rated to 500mA and your device needs 1A, then you will get 500mA and it will either not work or it will charge slower.
2.4A does not mean the charger is pushing 2.4A into your watch.
All this sounds like a cop out for something else going on.