You definitely need more power. It is a bad idea to source power to "heavy loads" directly from your Arduino's 5V output. That tops out at about 500mA and 6 servos can easily draw more than that especially when stalled or working hard.
Use a separate 5V power supply and connect its ground to the Arduino ground, but try to have as little common wire as possible between the servos and the Arduino. Ideally, there will be 2 ground wires coming from the power supply, one to the Arduino and one to all the servos.
The Quick Shield
: breakout all 28 pins to quick-connect terminals