I wonder if you could put some kind of gel padding under it to reduce vibrations. Kind of like what a gyro sits on. You probably don't want to use double sided tape because that would stay put and be a pain unless you wanted to it on the bird.
It's a thrift store. People donate goods and they sell it a yard sale prices. Normally the electronics are out dated and the cloths are usually 2 or 3 years old but still wearable.
Walt the video was not that bad. The camera almost added a vignette.