Since you are using a separate battery for the receiver you do not need, and shouldn't be using the ESC's BEC. UNless you disconnect the power lead in the ESC's cable to the receiver, you will still have the BEC trying to furnish power to the receiver, which is not good.
It appears that you have two choices, remove the separate receiver's battery and use the BEC (only one of them), or, disconnect the BECs and use the receiver battery. Give one of those a try. If it works, then which ever you didn't select ought to work too. Use which ever you prefer.
For some further guessing, since the problem only shows up when trying to run at full power, I'd have to guess that the 'main' (motor) battery is a higher voltage than the receiver's 4.8 volts. Am I right??
- 'Doc