Best way to deal with realistically imbalanced dataset for Regression problem
You said that "an object with label = 0 exhibits random looking motion...whereas those with label = 1 are highly ordered objects". If you can see that, why should your model not be able to? Just train it and see if it works.

However, your dataset does not seem to be very large. You should think about transfer learning from some pre-trained model if your images/objects are not too strange.

There is no a priori need to handle an imbalance of labels, just be sure to compare your loss to a proper baseline, e.g. the label mean.

You said you have additional features, append them after flattening the convolutional layers. If the additional features are also 2D, just add them as a channel to your Input.