How do I supply 200-ish mA to servo connected with Adafruit's PCA9685?
Looking at the application notes The logic on the PCA9685 should be powered from the same supply as the Raspberry Pi (3 - 5V) Vcc and this is low power. The servos can have their own separate supply V+ which can be as high as 12V if required. This can typically be a 5V 10A PSU and is connected to the PCA9685 via its V+ own connection block.

Each of your 3 wire servos has a control pin, a power supply pin for V+ and a common ground. They do not have to be powered from the same supply as the logic. Therefore all you need is a separate PSU with sufficient capacity to power your servos under full load.