Stuttering, sudden acceleration at low speed, MMP...

[suicideneil]

What firmware are you currently running?

Downgrading to v1.24 usually does the trick, otherwise an extra bank of caps on the input leads helps sometimes. An external BEC would only really help if it was the servo that was drawing too much current and causing the esc to reset due to voltage 'brown out'- a 'glitch-buster' capacitor plugged into the rx would be the first option to solve that issue before buying a BEC.

Might also be worth trying the torque control feature to reduce the current spike during acceleration, though that option is only available past v1.24 firmware ( try 'em all besides v1.28 which is a known esc borker... ).