This would be frustrating enough if I hadn't tried to re-flash the flight control board with new MultiWii software that then made the 'copter as unstable as an elephant riding a unicycle on a bouncy castle in an earthquake...
After lots of staring at code and running tests on my ECU, transmitter and motors, I noted that the accelerometer data lines on the multiwii config software were dancing all over the place. Remembering the bit of code in config.h:
/* MPU6050 Low pass filter setting. In case you cannot eliminate all vibrations to the Gyro, you can try
to decrease the LPF frequency, only one step per try. As soon as twitching gone, stick with that setting.
It will not help on feedback wobbles, so change only when copter is randomly twiching and all dampening and
balancing options ran out. Uncomment only one option!
IMPORTANT! Change low pass filter setting changes PID behaviour, so retune your PID's after changing LPF.*/
//#define MPU6050_LPF_256HZ // This is the default setting, no need to uncomment, just for reference
//#define MPU6050_LPF_5HZ // Use this only in extreme cases, rather change motors and/or props
I tried going through the low-pass filters until the wobbles seemed to be manageable using the 98Hz filter. I also balanced the motors, as these seemed to be creating much noise and vibration. I also added another layer of rubber grommets onto the flight controls mounting board. The results can be seen below on a kitchen table tethered flight: