Distributing power to many at once servos

Buck converters are best, because they loose less power. A liner regulator simply burns off the excess power as heat.

The Adafruit servo shield output FETs can't supply that amount of current, so you need to rethink the driver requirements from that. See the data sheet of the chip it uses for the complete solutions.
See:-
PCA9685.pdf

You also need to consider power supply decoupling thought the system.

See my tutorial at:-