Let's try something naughty
- Disconnect the external power supply from the PCA
- Disconnect all but one of the servos from the PCA and leave that one on channel 0
- Make sure that the servo can move freely so that there is no load on it
- Connect the V+ pin at the end of the PCA to 5V on the Uno
- Run the sketch that you posted
This is naughty because the servo is being powered from the Uno, which is not desirable, but I would be interested in knowing the outcome
If the servo sweeps as it should then remove power from the Uno after a few sweeps as we don't want to damage the Uno by having it supply too much current. Having said that, I have never had a servo cause a problem to an Arduino board when powered this way for testing but it is not a long term solution