Transition from clustering to classification?
In order to build a model to make predictions you need a labeled training set, that is, a training set in which each training example is assigned a class label. Training sets are usually labeled by human experts that use their domain knowledge to manually classify the examples in the training set. You have already done that, as described in your first paragraph. 

However, sometimes this process is expensive. In order to decrease cost sometimes semi-supervised learning is applied. In semi-supervised learning, and under some assumptions, a small amount of labeled, together with a large amount of unlabeled data, are used to build a predictive model. The unlabeled data are assigned labels during the training process. 

This seems to match your idea in your last paragraph, and it is already implemented in Python. I think that if you found clear clusters in your data it may work very well. Worth a try at least.